PHYSICAL REVIEW SPECIAL TOPICS - PHYSICS EDUCATION RESEARCH 3, 020109 共2007兲
Physics faculty beliefs and values about the teaching and learning of problem solving.
I. Mapping the common core
E. Yerushalmi*
Weizmann Institute of Science, Rehovot, Israel, 76100
C. Henderson*
Department of Physics, Western Michigan University, Kalamazoo, Michigan 49008, USA
K. Heller, P. Heller, and V. Kuo†
School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
共Received 28 October 2005; published 12 December 2007兲
In higher education, instructors’ choices of both curricular material and pedagogy are determined by their
beliefs about learning and teaching, the values of their profession, and perceived external constraints. Dissemination of research-based educational reforms is based on assumptions about that mental structure. This study
reports the initial phase of an investigation of the beliefs and values of physics professors as they relate to the
teaching and learning of problem solving in introductory physics. Based on an analysis of a series of structured
interviews with six college physics faculty, a model of a common structure of such beliefs for all physics
faculty teaching introductory physics was constructed. This preliminary model, when tested and modified by
future research, can be used by curriculum developers to design materials, pedagogy, and professional development that gain acceptance among instructors.
DOI: 10.1103/PhysRevSTPER.3.020109
PACS number共s兲: 01.40.Fk, 01.40.G⫺, 01.40.J⫺, 01.50.Kw
I. INTRODUCTION
Although significant curriculum development efforts for
at least four decades have produced materials and techniques
that have been shown to be more effective than those typically in use, they have had only a minor effect on the teaching of college-level physics.1–4 Even the most effective curricular materials, tools, and pedagogies must be accepted by
instructors if they are to become routine practice. This is
particularly true in higher education, where academic freedom gives faculty members a great deal of autonomy in
choosing both a curriculum and its teaching. It is curious that
this autonomy does not seem to give rise to a vast variety of
idiosyncratic introductory physics courses. Indeed, there appears to be a uniform and stable set of educational practices
in the teaching of introductory college physics that have been
characterized as traditional instruction.1 New instructional
ideas, such as those based on research in learning, must compete with these longstanding traditional methods.
In terms of the marketplace, improved educational products must gain customer acceptance if they are to displace
widespread traditional practices. In the commercial world,
product designers know that to gain market share, they must
construct their product to match the customer characteristics
that influence their choices. Following this model, the first
step of effective dissemination of curriculum or pedagogy
developed by physics education research must occur in the
design process. Acknowledging the knowledge, beliefs, and
values, as well as perceived needs and skills that underlie an
instructor’s choice of curriculum and pedagogy is a prerequisite to achieving a design that can be efficiently disseminated. 关Many researchers have decided that making the distinction between different aspects of teacher’s thinking is
1554-9178/2007/3共2兲/020109共31兲
neither possible, nor useful 共see, for example, Ref. 5兲. In this
paper, we will use the terms beliefs or belief structure to refer
to a general mental structure that involves knowledge, ideas,
beliefs, values, mental images, preferences, and similar aspects of cognition.兴
The purpose of our research is to begin the process of
building a model to describe the beliefs of physics faculty
that influence their choice of curricular materials and pedagogy when they teach introductory physics. It is anticipated
that this model can be used to formulate a set of testable
hypotheses that will lead to an elaborated and corrected
model with features that can be applied to curriculum and
professional development. The study reported here focuses
on the beliefs of physics faculty about the teaching and
learning of problem solving in the context of a calculusbased, introductory physics course. In particular, this study
investigates instructor beliefs that might affect their decisions to use research-based curricula that guide students to
develop expertlike problem solving, which functions as a
primary mode of learning introductory physics.6–11
A common feature of these research-based curricula12
is the use of a cognitive-apprenticeship instructional
approach.13–16 To implement this approach, instructors model
explicitly a general problem-solving framework that is implicit in the problem-solving approaches of experts,15 students attempt to solve problems within this framework while
being coached, and students practice using this problemsolving framework on their own. Students regularly reflect
on the modifications that they made to their initial problemsolving process. Even though data shows that these researchbased curricula achieve their goals,8,17 only a minority of the
instructors who profess to emphasize problem solving in
their courses adopt them.
020109-1
©2007 The American Physical Society
PHYS. REV. ST PHYS. EDUC. RES. 3, 020109 共2007兲
YERUSHALMI et al.
II. BACKGROUND
A. Beliefs of college faculty
A number of researchers have investigated the general
ideas of teaching held by college instructors.1,2,18–20 All of
these studies result in a hierarchical list of different ways that
the instructors understand teaching. The lists differ in detail,
but they range from teacher-centered ideas of learning, resulting in instruction emphasizing the transmission of knowledge, to student-centered ideas tending toward the constructivist approach. There is some research on instructors’ views
about learning and teaching in the context of physics problem solving. In one study, 24 Australian physics and chemistry instructors were interviewed about issues related to their
ideas of teaching and learning in first year university science
classes.21 Seventeen of these instructors talked explicitly
about problem solving. This data indicated that instructor
beliefs about problem solving were correlated with their
ideas about teaching. Instructors who thought of problem
solving as an application of existing knowledge held more
teacher-centered views of teaching, while instructors to
whom problem solving was about making sense of the problem held more student-centered views. University physics
and chemistry teachers who taught service courses were
more likely to have a teacher-centered idea of teaching than
those who taught graduate students.2,18 Other studies on
physics instructors, however, report very different
conclusions.4,22 For example, one study reported that physics
instructors believed that the introductory physics course was
primarily a framework for students to develop their individual intellectual skills.22 Unfortunately, all of these studies
are too general to provide much information useful to curriculum developers.
B. Beliefs of K–12 science teachers
Studies of K–12 teachers found that their beliefs were not
necessarily reflected in their classroom practice because conflicting ideas often arise when teachers consider a possible
instructional activity from different perspectives.5,23–25 For
example, one study of 107 K–12 science teachers found that
teachers believed that including cooperative learning in the
classroom could help increase student learning, make science
more interesting, increase problem-solving ability, and help
students learn cooperative skills.25 But they also believed
that the use of cooperative learning would increase student
off-task behavior and take up too much class time. The study
found that the concern for off-task behavior was the best
predictor of a teacher’s intention to use cooperative learning.
A study of eight Israeli high school physics teachers regarding their ideas about the learning and teaching of problem
solving revealed that they were aware that students needed to
develop processes for problem solving, yet their ideas about
instruction did not include the development of those
processes.26
Research about teachers’ decision-making process shows
that they draw upon tangled and occasionally conflicting
conceptions.5,23–25,27 Teachers’ decisions seem to be shaped
by a constellation of beliefs, goals, knowledge, and action
plans.28 Each decision depends on the immediate context,
interpreted in light of former experiences. Much of an experienced teachers’ decision making is automated, and the
teacher is no longer aware of the reasons that led to its
development.29–32 To collect meaningful data about teaching
and learning beliefs, these studies found it necessary to develop tools that probe teachers’ ideas at different levels and
from different directions.
An effective data collection tool to study a teacher’s beliefs about teaching and learning was to ask them to make
decisions in actual or simulated teaching environments.29–34
This tool was found to be superior to observing them teach
because they could be asked to “think aloud” and explain
their interpretation of events and resulting decisions in real
time. This technique is similar to the methodology used in
many studies of students’ conceptions of scientific
phenomena.35–40 In these studies, students are asked to interpret and explain specific events, usually using concrete artifacts. The researchers infer student ideas from these responses.
C. Dissemination models
The lecture/demonstration mode of teaching used by a
vast majority of physics faculty, especially when teaching
introductory physics, appears to imply a transmission model
of teaching and learning: the instructor carefully explains a
concept or technique, sometimes using examples or demonstrations, and the conscientious student understands and can
use that idea or technique.41 Their students then practice, do
homework, until that usage becomes automated. Dissemination efforts for new curricular materials or pedagogical techniques often begin by attacking that transmission model and
developing a rationale that favors a constructivist view of
teaching and learning, which is the hallmark of many reform
curricula. The constructivist view proposes that each student
constructs his or her own knowledge by interpreting instruction in terms of their existing knowledge structure and
changing parts of that knowledge structure.42
A common type of dissemination seeks to create a cognitive disequilibrium between the instructor’s teaching goals,
their assumed schema of transmission as teaching, and evidence of student performance that traditional instruction does
not meet the goals. This disequilibrium is then resolved in
favor of a specific constructivist approach. The activities incorporated into this type of dissemination are based on the
assumption that faculty teach in a mode that emphasizes the
transmission of information because they believe that this is
an effective mode of teaching and learning or that they value
this mode of instruction. However, physics instructors often
revert to traditional teaching practices, even when they attended professional development sessions that take this approach and use the new curriculum in their classrooms.23
This is true even when the instructional support for the new
curriculum exceeds that available for traditional materials.
The observation of transmissionist instructional practices
does not, however, necessarily mean that these instructors
have transmissionist beliefs about teaching and learning. In
fact, several studies suggest that dissemination activities
aimed at teachers’ assumed transmissionist beliefs have not
020109-2
PHYSICS FACULTY BELIEFS AND… . I. …
PHYS. REV. ST PHYS. EDUC. RES. 3, 020109 共2007兲
produced widespread instructional change in K–12 teachers
because of the complicated and sometimes inconsistent nature of teachers’ beliefs.5,24,43–46 Although less research exists
for college instructors, data indicate that they are similar to
K–12 teachers in this respect.23 Other findings suggest that
instructors’ beliefs color their perception of classroom events
so that what they are actually doing is not necessarily what
they intend to do. Even when some instructors use a constructivist curriculum, their practice often alters its original
intent.47–52
If college faculty also have a complex belief structure for
instruction that is not necessarily internally consistent and
not determined by large overarching schemas, then there are
three strategies to disseminate effective instructional models.
In order of their implementation difficulty from easiest to
more difficult, these strategies are:
共1兲 Design new curricular materials and their accompanying pedagogy to be as consistent as possible with existing
instructor beliefs and avoid conflict with strongly held beliefs.
共2兲 Design short professional development workshops to
reinforce faculty ideas that align with the proposed curricula,
while weakening undesirable beliefs by pointing out internal
conflicts and using the standard methods of persuasion to
support the desired beliefs.
共3兲 If the instructional design violates key instructor beliefs and practice, design a thorough professional development to accompany and support a long term process of
change.
In all cases, it is first necessary to determine the faculty
belief structure that underlies their instructional decisions.
III. RESEARCH QUESTIONS
This study is the initial step in building a model of the
common underlying belief structure of university and college
physics professors with respect to the use of problem solving
when they teach introductory physics. The first, and most
important, issue for this line of research is to determine
whether there is a limited set of belief structures that can
describe most physics faculty. It is possible that instructors
do not have a common core of beliefs with respect to teaching and learning, since they have no formal education in this
domain and typically do not discuss their teaching beliefs
with colleagues. On the other hand, it is possible that instructors do have a common core of beliefs about teaching because they received their education from a limited group of
universities at which they had similar educational experiences.
If there is a common core, then our initial model of this
core should encompass three general features of an instructional system:53 共1兲 the initial state of the students with respect to their knowledge and skills in solving physics problems, 共2兲 the desired final state of the students, and 共3兲 the
instructional processes necessary to accomplish the transformation from the initial to the final state. This systems approach commonly underlies research-based curriculum in
physics problem solving.6–11 We should be able to represent
the complex interrelationships among instructor beliefs and
discriminate between strongly held and fragmented or even
conflicting beliefs. Hence we should answer the following
questions:
共1兲 What do instructors believe students should do when
solving problems?
共2兲 How do instructors believe students should learn in
the context of problem solving?
共3兲 What prerequisite knowledge or skills do instructors
expect of their students?
共4兲 How do instructors characterize their students’ actual
learning and problem-solving practices?
共5兲 How do instructors believe they could help students’
learning in an optimal situation?
共6兲 What do instructors think limits their instruction?
共7兲 How do instructors weigh their values, beliefs, and
perceived constraints to arrive with their actual instruction?
As additional guidance for the curriculum developer, it is
useful to know how instructor beliefs align with the assumptions that underlie research-based curriculum and with the
standard instructional paradigms,16 behavior, developmental
共constructivism兲, and cognitive apprenticeship.
IV. METHODOLOGY
Considerable measurement and analysis challenges face
researchers investigating the beliefs that influence the instructional decisions of physics faculty. Observations can be
misleading because a person’s practice reflects their resolution of many different and potentially conflicting ideas. Indeed, observation of people’s behavior is typically not useful
in determining the necessary elements for changing that behavior. Questions about beliefs, whether written or oral, often do not uncover unanticipated or implicit ideas that might
underlie decision making. General interviews about beliefs,
in which the interviewer explicitly probes for those ideas,
can give results that are biased by the belief structure of the
interviewer. For this study we drew on the techniques of
ethnography,54 particularly as applied in policy capturing
techniques,55 to design artifact-based structured interviews.
We also drew on the grounded theory approach to qualitative
research56,57 for analysis principles such as the constant comparison method of inductively developing emerging categories and their relationships from the available data. Of
course, any interview risks biasing the data by imposing the
interviewer’s expectations on the discussion; hence the data
collection and analysis tools were carefully designed to bring
out the authentic views of the interviewee. A brief overview
of the methodology is described in the following sections,
and a full description is provided in the companion paper.58
A. Data collection
The interview encouraged introspection by asking for a
comparison among artifacts. We used specific familiar instructional tools as artifacts. Those artifacts, shown in the
companion paper,58 were built from actual materials used by
020109-3
PHYS. REV. ST PHYS. EDUC. RES. 3, 020109 共2007兲
YERUSHALMI et al.
physics faculty while teaching introductory physics. All of
the artifacts were built around a single physics problem that
was given to students on an introductory, calculus-based final
examination. The problem was sent to each instructor before
the interview and they were asked to solve it as preparation
for the interview. The artifacts for the interview consisted of
five different versions of the same problem, three different
instructor example solutions for the problem, and five different student solutions. The artifacts, although based on authentic documents, were constructed to reflect the range of
instructor practices. They were also designed to reflect differences between: 共1兲 traditional and research-based curricula in the arena of problem solving;59,60 and 共2兲 the three
basic instructional paradigms,16 behavior, developmental
共constructivist兲, and cognitive apprenticeship. The method of
using comparison tasks aims to focus the discussion and
elicit implicit beliefs, hence minimizing the randomness of
the interviewees’ commentary. Another advantage of comparison tasks is that they use only natural language and avoid
“leading questions” that might bias the responses.
The interview took about 1.5 hours to administer and had
four parts. The first three parts dealt with different instructional situations: 共1兲 the instructor assigns a problem to students; 共2兲 the instructor grades a student’s solution; and 共3兲
the instructor presents students with an example problem solution. To minimize subjectivity, an initial plan for interviewer interventions was predefined and scripted. The interviewer added probing questions to make sure the interviewee
answered the predefined questions. In each part of the interview, general questions were asked about how and why the
instructor might use a specific type of artifact and how the
artifacts compared to the materials actually used in their
classes. The interviewee was also asked to reflect on the
problem-solving process as represented in these artifacts.
During the interview, the interviewer wrote on index cards
each feature of the problem-solving process that the instructor mentioned. In the last part of the interview the instructor
was asked to group these index cards into categories of their
choosing and name the categories. The interviewer then
asked several questions regarding these problem-solving categories to determine if the instructor thought they were reasonable to expect of their students, how instructors thought
that students could overcome any difficulty they had with
them, and how the instructor could help students with these
difficulties. Finally, instructors were asked about their satisfaction with their current course. Triangulation was accomplished by comparing the interviewee’s statements among
the different types of artifacts and with the final classification
task. Both the audio and visual content of the interview was
recorded on video and the audio portion was transcribed.
B. Sample
The results presented in this paper are based on interviews
with six instructors. These instructors were randomly selected from a pool of 23 instructors from the University of
Minnesota who had taught the introductory, calculus-based
physics course at least once in the past 5 years. This group
was chosen as a calibration group for the study because their
instructional behavior was known. A group from a single
institution was chosen to form an initial model because they
had the largest chance of having coherent beliefs about
teaching and learning. All of the participants were male.
They had a broad range of teaching experience 共2 – 43 years兲,
as well as experience teaching the introductory calculusbased course 共1–79 times兲.
These instructors teach at a research university with an
active physics education research group. During the previous
12 years, this research group had introduced significant
changes to the introductory, calculus-based physics
course,8,9,61 while leaving the underlying structure of lectures, discussion sections, and laboratories in place. These
changes have been shown to be effective in improving students’ problem-solving skills as well as their understanding
of physics concepts,8,9,62 and continue to be the framework
of all introductory physics instruction in the department. Although the teaching assistants 共TAs兲 for these courses receive
instruction and support for teaching problem solving in cooperative groups,62 the professors did not.
No constraints were put on the professor about how lecture time should be used. They were responsible for meeting
with their TAs weekly and organizing the laboratories and
discussion sections as well as their lectures for their course.
Although various changes in the role of the professor had
been suggested and modeled within the department, almost
all faculty conducted their lectures in a manner that would be
described as “traditional.” Observations of these instructors,
including one detailed study,63 confirmed that their style of
teaching was best characterized as transmission. Nevertheless, it is likely that the instructors interviewed for this study
are more knowledgeable about the teaching and learning of
problem solving than instructors at other institutions because
of their exposure to the curriculum implementation activities
of the physics education research group.
C. Data analysis
Analyzing the rich data derived from the interviews posed
several challenges, the first of which was to determine how
to efficiently represent the complex interrelationships among
the instructor beliefs underlying the interview narrative. To
address these challenges, we developed an analysis technique
involving a version of open coding57 to construct multilayered concept maps. This analysis technique is described
briefly below, and in more detail in the companion paper.58
The analysis consisted of the following four steps.
共1兲 Each instructor’s interview transcript was broken into
statements64 that addressed one or more of the predefined
research questions. This step was performed independently
by at least two members of the analysis team until an agreement rate of 93% was achieved. Each of the interviews
yielded approximately 400 statements.
共2兲 A tentative concept map65 was constructed from the
transcript statements of the six instructors. Each box represented a principal category of an instructional system53 for
the learning and teaching of problem solving; the links 共arrows兲 between the boxes represented the relationship between these categories that we found prominent in the transcripts. We call this the “main” map.
020109-4
PHYSICS FACULTY BELIEFS AND… . I. …
PHYS. REV. ST PHYS. EDUC. RES. 3, 020109 共2007兲
共3兲 Individual concept maps were constructed for each
instructor to elaborate each principal category on the main
map. All statements related to each principal category were
sorted and categorized via confined open coding.58 Analysis
was constrained by the research goals by matching instructor
statements to the tentative main map whenever possible. It
was still, however, an open coding process57 where
instructor-generated categories and connections were allowed to emerge. Thus the main map and the individual concept maps were modified as new categories or connections
were uncovered in the analysis of other instructor’s transcripts.
共4兲 For each principle category, a concept map was constructed to represent the commonalities and differences of
the concept maps of each instructor. We called these “composite” maps 共see Fig. 2兲.
Each step included a validation process in which at least
one additional researcher returned to and reinterpreted the
original statements used to build a map. The entire research
team discussed and resolved all disagreements. This process
resulted in the iterative revision of the concept maps until all
statements of each instructor fit into all of the composite
maps.
It is important to keep in mind that, although the boxes
共representing the principal categories兲 and the connections
between them 共represented by links between boxes兲 came
directly from the interview data, this organization is a construct of the analysis process. The organizing structure
shown in the maps was not provided explicitly by the interviewees. They did not necessarily directly express either the
main ideas on the maps, nor their connections. Consequently,
the maps should not be read as evidence of a conscious organization of the beliefs of any specific instructor. It is unlikely that any of the individuals interviewed envisioned the
entire picture of their belief structure.
V. RESULTS
The composite concept maps are the most direct representation of the results of this study. Taken together, they represent a model of the underlying beliefs about the role of problem solving held by the population of physics faculty
teaching introductory calculus-based physics. The concept
maps show those factors that faculty believe are important
共the boxes兲, and how these factors are linked 共the lines兲. In
cases where there might be more than one major set of beliefs in the faculty population, the maps show the alternatives. In Sec. A–H below we give interpretations of the concept maps with respect to the seven research questions that
motivated this study. We have also included some of the raw
data to illustrate the basis of these interpretations.
A. Overview of instruction and learning
The main map, shown in Fig. 1, is a model of the common underlying belief structure of university and college
physics faculty with respect to using problem solving when
they teach introductory physics. This map is the initial step
in building testable hypotheses addressing the categories and
links of the model. Clearly, the main map and its associated
composite maps are influenced by the structure of the interview and the analysis. However, because the main map reflects the instructors’ discourse in relation to the questions
and artifacts of the interview, we believe that such a map,
when tested and modified, will be a useful representation of
the underlying pattern of common instructor thought that
must be respected in any attempt at curricular change. By
explicitly showing a model of these beliefs and how they are
linked, the specifics of the map can be tested by more directed experimental means. By using the iterative analysis
technique described in the companion paper,58 we found
such a large degree of similarity that we were able to build a
common main map as well as composite maps that illustrate
prevalent instructor similarities and differences.
The most important conclusion of this study is that these
physics faculty have a very similar belief system about the
teaching and learning of problem solving in their introductory physics classes. The instructors’ belief system is most
closely aligned with extreme constructivist learning theories.
This is not to say that any of these instructors have a carefully constructed “teaching philosophy.” As with any human
thought, instructors’ belief systems have parts that are internally inconsistent and reveal gaps where parts do not obviously connect to other parts. Although instructors have a
large overlap in their belief systems, they are not identical.
Some important characteristics of the main map are described briefly below. Further elaboration is provided in the
following sections 共B–H兲.
1. Typical students’ learning practices differ dramatically from
those required for the course
At the top of the main map are two boxes 共principle categories兲 focused on students’ characteristics: the category
“Students Who Can Improve” 共elaborated in Fig. 7兲 and the
category “Typical Students” 共elaborated in Figs. 8 and 9兲.
The category “Students Who Can Improve” and its links
shows that the instructors do not expect their actions to influence all students in their classes. Instructors usually exclude students who can learn without instruction and those
who do not have enough “natural ability” to learn with instruction. Most instructors believe that, while most students
in their class are intelligent enough to construct the “Appropriate Knowledge” 共Fig. 3兲, only a fraction of those actually
do so. These target students, who do improve meaningfully,
are those that enter the course with the motivation to work
hard, are confident about their ability to learn in the course,
and have good study habits, namely an ability and inclination
to be reflective.
The “Typical Students” composite map describes the instructor beliefs that typical students’ learning practices differ
dramatically from those that they think students need for the
course. In general, instructors believed that typical students
have poor problem-solving skills and detrimental learning
characteristics. In particular, they thought that typical students did not engage in reflective learning. One instructor
explicitly described this mismatch by contrasting the typical
student with his target audience:
020109-5
PHYS. REV. ST PHYS. EDUC. RES. 3, 020109 共2007兲
YERUSHALMI et al.
“The 关typical兴 students who are required to take the
physics course and reject it as much as they can and
are happy if they pass are the kinds of students I have
to deal with—they are the bread and butter of the
department…they’re not going to work hard… they’re
just riding along.” 关I2, 42, 37兴
“I am mainly interested in the students who respond to
the class.” 关I2, 40兴.
The notation 关I#, #兴 denotes 关Instructor identification number, Transcript statement number兴.
2. One learns problem solving by being reflective, yet reflectivity
is beyond the scope of the course
Problem solving was discussed by the instructors in two
distinct ways: in the box “Solving Physics Problems” 共Fig.
2兲 as a worthwhile activity on its own, that serves as a goal
for the course; and in the box “Work” 共Fig. 4兲 as the principle tool to reach many of the other course goals. The
“Solving Physics Problems” composite map represents the
problem-solving process that instructors hope the students
they target will be able to perform at the end of the course.
The goals of the course, as presented in “Appropriate Knowledge” composite map 共Fig. 3兲, included the correct understanding of physics concepts as well as effective problemsolving approaches and techniques. The central belief of the
instructors was that students learn to solve problems by engaging in problem solving and reflecting on it. All instructors
thought students should also “Use Feedback” 共Fig. 5兲 or
“Look/listen” 共Fig. 6兲 to the instructor’s “Appropriate Example Solutions” 共Figs. 11 and 14兲. But they did not believe
that students can learn problem solving solely by these actions. Reflectivity was brought up as a specific way of working, using feedback or watching someone demonstrating
problem solving, that is required to fully utilize these experiences to construct the appropriate knowledge. Even though
all the instructors mentioned a category of reflective skills
共self-evaluation兲 as a prerequisite for learning using problem
solving, they viewed this skill as beyond the scope of an
introductory physics course. Nevertheless, the instructors estimated that a majority of the students attained most other
categories of appropriate knowledge by the end of the
course.
3. Instruction is not designed to promote reflectivity, which is
required for learning
Instructors were viewed as either: 共1兲 providing resources,
such as problems for students to solve and instructorgenerated example problem solutions, 共2兲 imposing constraints on students 共e.g., grading homework兲, or 共3兲 giving
suggestions on how to approach learning and solve problems
effectively. The main map shows a link between the “Typical
FIG. 1. 共Color兲 Main map of faculty beliefs and values about learning and teaching problem solving in an introductory physics course.
Boxes and links on the main map are common to all six instructors. The boxes framed with a double line indicate principal categories that
are elaborated in separate composite map figures, as indicated.
020109-6
PHYSICS FACULTY BELIEFS AND… . I. …
PHYS. REV. ST PHYS. EDUC. RES. 3, 020109 共2007兲
Students” box and the instructors’ actions, reflecting that the
resources that instructors provided were, they believed,
adapted to some extent to accommodate the typical student
characteristics. For example, the belief that entering students
could solve only one-step problems led some instructors to
assign only one-step problems at the beginning of the course.
In their lectures, instructors reported that they occasionally
told students to work reflectively. They did not constrain
them to do so, even though they believed learning requires
reflectively engaging in problem-solving activities, and that
typical students do not have reflective skills.
Instructors’ ideas of appropriate teaching actions were determined primarily by their values in the domain of physics,
their beliefs of how students might react negatively to alternative actions, and their recognition of their own limitations.
For example, although they thought students would learn
better from example problem solutions that contained more
explanation of expert thought processes, they refrained from
constructing these solutions for three reasons: 共1兲 their physics values directed them to not stifle student creativity in
problem solving by providing solution examples that were
too detailed; 共2兲 they believed that students would be frightened by problem solutions showing too many steps; and 共3兲
they did not have the time to construct such solutions. Several instructors also expressed the belief that they did not
have the knowledge required to make up “good” problems,
which they believed would differ from those in the textbook.
The following 共Secs. B–H兲 is an elaboration of these results that address the research questions posed in Sec. III.
1. Problem solving as a process
Three instructors described the process of solving physics
problems as a linear decision-making process, two believed
it was more of an exploration process, and one had a mixture
of both.
The linear decision-making process was described by
three of the six instructors and involved the following stages.
共a兲 Stage 1. Identifying the relevant physics principles and
concepts:
“Dealing with a problem is standardized into a number
of steps: a, what are the physical principles that operate
in this situation.” 关I2, 84兴
For some, this identification entailed first categorizing the
problem and than retrieving pieces of knowledge related to
the category.
“Having categorized a problem, the category then
brings up to me a bunch of stuff related to the category.” 关I5, 77兴
We found that the categorization could involve either physics
concepts or surface features, and the phrasing of the related
pieces of knowledge was sometimes vague and potentially
misleading.
“For example, in a potential energy problem, generally
you have to match the potential energy to the kinetic
energy or something like that.” 关I5, 77兴
“They’ll look at it and say ‘Hey, that’s like these loopthe-loop problems.’ These problems are nice because
it’s always a normal force and the normal force is always perpendicular to the direction.” 关I3, 119兴
B. What do instructors believe students should do when
solving physics problems?
Our model about what instructors believe their students
should do when solving physics problems comes from two
data sources: 共1兲 the components of problem solving that the
instructors described when they looked at and discussed the
interview artifacts; and 共2兲 the categories of problem solving
that instructors provided in the final part of the interview,
when they sorted their own problem-solving components
into categories. When discussing the interview artifacts, instructors typically described the components of problem
solving as elements of a “process.” We grouped these components in the box “Solving Physics Problems” 共Fig. 2兲.
During the final part of the interview, after the instructors
had sorted their problem-solving components into categories,
they were also asked: “Which of these things 共categories兲 is
it reasonable to expect most students to be able to do by the
end of the introductory, calculus-based physics course?” and
“Where are your students regarding these categories when
they enter the course and in the end of the course?” these
questions assumed that some of their problem-solving categories function as goals. This assumption was supported by
the fact that the instructors estimated to what extent their
students’ achieve some of the categories. When they felt a
category was not actually a goal of their course, they said so.
We grouped the goal categories 共represented in uppercase兲 in
the “Appropriate Knowledge” box, Fig. 3. Each of these
views, problem solving as a process and problem solving as
a course goal, are described below.
The recognition process can take a systematic hierarchical
structure, and can be facilitated by a visual representation of
the problem situation.
“I think that a lot of solving physics problems can be
enhanced by essentially using some sort of tree structure in their thought process.” 关I5, 73兴
“I can draw a diagram to clarify my thinking.” 关I2, 84兴
共b兲 Stage 2. Applying specific techniques: “Combining
these 共drawings principles兲 into a mathematical form that can
come up with the final answer.” 关I2, 84兴
共c兲 Stage 3. Evaluation of the answer: “I encourage students to check dimensions; I would say ⬘make sure you have
a force when you’re done with this thing’.” 关I3, 11兴
The exploration process was described by two of the six
instructors and involved coming up with possible choices
and then testing them.
“In solving a problem you need to have some vague
idea in your mind about what you need to do and then
come up with the explicit tools.” 关I1, 103兴
“You’re often playing around with it for a while to see
what approaches might be valuable if you’re not an
expert at it.” 关I6, 147兴
Making mistakes and having to backtrack and clarify under-
020109-7
PHYS. REV. ST PHYS. EDUC. RES. 3, 020109 共2007兲
YERUSHALMI et al.
FIG. 2. 共Color兲 “Solving Physics Problems” composite map of faculty beliefs about the problem-solving process in an introductory
physics course. Numbers in the parentheses denote the instructor whose statements directly justify that category. Uppercase labels refer to
specific types of knowledge that also occur in the “Appropriate Knowledge” composite map shown in Fig. 3.
standing is a natural part of problem solving. For example:
problem:
“Solving a problem is not a logical process—there’s
something that you have to guess and then use trial and
error.” 关I1, 28兴
“Solving physics problems is an art and we should
think of it as an art… . Each physics problem has a
kind of style to it, a gestalt to it.” 关I4, 101兴
The sixth instructor described the problem-solving process as artfully crafting a unique solution for each
Yet he also shared some features of the other two perspec-
020109-8
PHYSICS FACULTY BELIEFS AND… . I. …
PHYS. REV. ST PHYS. EDUC. RES. 3, 020109 共2007兲
FIG. 3. 共Color兲 “Appropriate Knowledge” composite map of faculty beliefs about problem-solving goals in an introductory physics
course. Numbers in the parentheses denote the instructor whose statements directly justify that category.
tives. He had the exploration idea that evaluation and backtracking is part of problem solving:
“I favor for the students to leave quantities in symbolic
form until the end. That will enable them to spot errors.
If something doesn’t make sense, they can spot the
symbolic forms of these things and, for example, look
at the dimensions and see whether they make sense.”
关I4, 69兴
He also believed that you start a solution process by connecting specific situations to general physics principles.
“Another tool that you want to carry with you, which I
think a reasonably sophisticated student would realize,
is that one of the clichés is that tension on a string, on
an object that’s going around in a circle, doesn’t do any
work. The motion is at right angles to the force.” 关I4,
36兴
who believe their students should use an exploration process
appears to be the expectation of the success that the students
will have at each step of the problem-solving process. At one
extreme, instructors who want their students to follow a linear process believe their students should make the correct
decision from one step to the next. At the other extreme, the
instructors who believe their students should follow a process of exploration assume that each student decision might
be incorrect. For these instructors, exploration is necessary to
make a correct choice from a collection of possibilities. They
do not envision students employing an organized procedure
that will limit choices and determine when important decisions must be made.
2. Problem solving as course goals
The difference between the instructors who believe their
students should solve problems by a linear process and those
The problem-solving categories that function as goals for
the course are shown in the map “Appropriate Knowledge,”
Fig. 3. They yielded four different types of appropriate
knowledge that most instructors shared. In the following,
instructor statements written down by the interviewer during
the interview for use as the final artifact in the interview
process are not given transcript numbers.
020109-9
PHYS. REV. ST PHYS. EDUC. RES. 3, 020109 共2007兲
YERUSHALMI et al.
共1兲 The APPROACH TO SOLVING A PROBLEM category was shared by all instructors. They labeled this category as “Overall Approach/Philosophy” 关I1兴, “Strategy” 关I2,
I3兴, “Organizing work” 关I4兴 or “General approach” 关I5兴. Instructors included in this category items of the following
types.
共a兲 Initial analysis of the problem: Translating English
statements to physics/math equations 关I1兴, Summarize
knowns and unknowns at beginning 关I4兴, Identify physics in a
problem situation 关I3兴, and Categorize the problem 关I5兴.
共b兲 Devising a plan: Break the problem into steps 关I1兴;
Assembling steps 关I2兴; Follow some strategy 关I3兴; Develop a
strategy to arrange principles 关I4兴; Organize decisionmaking on a tree structure 关I5兴; Identify physical concepts
关I3兴, and Categorize problems 关I5兴.
共c兲 Thinking over the plan: Explore yourself what you can
do with physics ideas 关I1兴; Analyze each step 关I2兴; Reasoning
process 关I3兴; and Think about problem in a logical way 关I5兴.
共2兲 The category “PHYSICS CONCEPTS” was shared by
all instructors. It was labeled so by I3, and also as “Understand Physics” 关I1, I6兴 or “Big Principles” 关I4, I5兴. It included items like Knowing conservation of energy [everybody], Know physics laws and limits of application 关I1兴.
共3兲 The “SPECIFIC TECHNIQUES” category was shared
by four instructors. It was labeled so by instructors I1 and I5,
and also called “implementation” 关I2兴 and “procedural” 关I6兴.
It referred to a student’s ability to perform technical processes after deciding on a path to take while solving a problem. Instructors included in this category statements such as
Good algebra skills 关I1兴, Substitutes to get answer 关I2兴,
Draw vector diagrams 关I6兴.
共4兲 The SELF EVALUATION category was shared by five
instructors. It was labeled by them as “Big Picture Technique” 关I1兴, “Perspective” 关I2兴, “Signs of Maturity” 关I3兴, and
“Hope students do” 关I6兴. It included statements that refer to
an ongoing evaluation of the process: Need to evaluate if
right direction 关I1兴, Recognize when something is missing
关I3兴, Have a doubt when unsure, and Play around to see
what approaches might be valuable 关I6兴. It also included the
evaluation of the final answer: Translate back to see if meaningful 关I2兴, and Realize that final result is large 关I6兴.
Another category was not explicitly defined by the instructors in the card categorization process but emerged
when analyzing the transcripts. Three of the instructors included in their discourse on appropriate knowledge statements concerning professional physicist beliefs about problem solving.
共5兲 The professional physicist beliefs category about problem solving includes the understanding that problem solving
involves exploration and that most problems cannot be
solved in a single step: “this idea that there’s an exploratory
process to do it is a professional type approach to do this sort
of thing” 关I6, 255兴.
All instructors, whether they expected their students to
use a linear or an exploratory problem-solving approach, desired that their students use strategic problem-solving skills
such as initial analysis, planning, and self-evaluation. They
believed that most of their students did not have these skills
when entering the course, and only had a partial grasp of
them by the end of the course. However, none of these instructors expressed the students’ need to learn these strategic
problem-solving skills when faced with our artifacts. Their
recognition that students needed to learn strategic problemsolving skills only surfaced when the instructors were asked
to sort their previous statements about problem solving.
From this we infer that the instructors’ belief that their students need to learn such skills was not strongly linked to
their beliefs about teaching actions.
C. How do instructors believe students should learn in the
context of problem solving?
All instructors believed that the primary way students
learn problem solving in introductory physics is by working
on problems. The composite map “Work” 共Fig. 4兲 includes
instructors’ beliefs regarding using problem solving as a process directed at learning. This information comes primarily
from three places in the interview process: statements that
they provided when reacting to the different interview artifacts; response to the interviewers’ prompting about the difficulties students had with each of their sorting categories;
and their goals as stated in the final part of the interview.
All instructors expressed the belief that a student can get
the appropriate knowledge by working problems, typically
many problems.
“I’ve always just thought doing a lot of problems is
important.” 关I6, 236兴
The instructors often expressed their belief about how students should work problems by contrasting it with what they
believed to be typical student behavior.
“Students spend large numbers of hours just doing
problems but not doing them with a disciplined approach.” 关I4, 51兴
They were all able to elaborate their ideas about effective
student practice. For example, the “disciplined approach”
was a reflective approach.
“Ok, that’s the way you do problems, you write equations. All right, after you’ve written an equation do you
have a clear understanding of why you wrote that and
not something else? I would call it studying with a
constant focus on the principles.” 关I4, 51兴
Instructors thought that practicing should be done on one’s
own, with minimal help while clarifying difficult points with
peers.
“What I often say is that they have to solve problem
without looking at solutions, and if they get stuck, talk
to someone specifically about what the next step would
be, rather than looking at solutions, so they don’t get
too much help, which lets them get away without actually thinking on their own.” 关I1, 321兴
They wanted the students to do something different than
merely solving problems.
020109-10
PHYSICS FACULTY BELIEFS AND… . I. …
PHYS. REV. ST PHYS. EDUC. RES. 3, 020109 共2007兲
FIG. 4. 共Color兲 “Work” composite map of faculty beliefs about learning from working problems. Numbers in the parentheses denote the
instructor whose statements directly justify that category. The boxes framed with a double line indicate principal categories that are
elaborated in other composite maps. Uppercase labels refer to specific types of knowledge that also occur in the “Appropriate Knowledge”
composite map shown in Fig. 3.
prerequisite for learning by any other means.
“I often tell students that if they are having difficulty
that what they should do is look at a lot of problems,
not necessarily work them, but look at the problems,
and then go through the strategy part of the problem
saying to themselves ⬘what do I need to know for this
problem, and what are the parameters that are specified, and what are the things that I have to calculate or
that I have to know in order to solve this problem.’ If
the student thinks that he knows these things then he
can go to the next problem. He shouldn’t do the implementation and actually come to a number.” 关I2, 279兴
“I hope that they are in the habit of looking at the
homework problems and trying to do them and then
when they come to class they either have already done
them or they are learning something from my solving
the problems and it’s not just another example that I’m
doing on the blackboard.” 关I2, 143兴
Or as another instructor phrased it, practicing should involve
consciously generalizing.
“I try to get students to think consciously about their
general approach. I want the students to be able to
verbalize their general approach, and not just sit and
wait for lightning bolts to strike.” 关I5, 313-314兴
Four of the six instructors believed that working problems
is the best way to attain the goals of the course and is also a
In addition to reflectively working problems, most instructors believed that it was useful for students to get direct
feedback and to see examples of problem solving either from
lectures or from written material. The interview artifacts, student problem solution and example instructor solutions, directly prompted responses about students working problems,
the utility of written examples, and students’ processing of
instructors’ grading. However, remarks about other types of
feedback and the role of lectures were spontaneous. Many of
the statements on feedback centered on grading, and have
been previously published.66 The composite map “Using
Feedback” 共Fig. 5兲 elaborates the instructors’ beliefs about
the process of feedback in student learning, whether from
020109-11
PHYS. REV. ST PHYS. EDUC. RES. 3, 020109 共2007兲
YERUSHALMI et al.
FIG. 5. 共Color兲 “Use Feedback” composite map of faculty beliefs about learning from using feedback. Numbers in the parentheses denote
the instructor whose statements directly justify that category. The boxes framed with a double line indicate principal categories that are
elaborated in other composite maps.
grading and comments on students’ test solutions, instructors’ coaching in office hours, or from discussion with peers
in study groups.
Most instructors wanted their students to compare their
own work to an instructor’s example solution. Some believed
that students needed to go through a detailed analysis process.
“Ideally, I suppose, that students would analyze their
test solution and maybe my test solution to see where
the major differences are, and then try to work on it.”
关I1, 136兴
“Look at a solution and get something out of it by
looking at the structure of the problem, what concepts
are addressed.” 关I3, 45兴
“Ideally, when students see my solutions, I would like
them to think about what’s going on. That would be
my main goal, is if they can be thinking why is this
step going from one step to another.” 关I6, 23兴
Most instructors believed that learning physics happens
slowly, but not incrementally in the sense of behaviorist
accumulation.16
Other instructors seemed to believe that students could learn
from just looking at the instructors’ solution.
“If the students can’t solve a problem, then the solution
that I give them should show them how one could
solve the problem, with the hope and expectation that
the next time they saw something similar they would
have in mind a method that they might apply to it.” 关I5,
30兴
The instructors also believe there is a role in the learning
process for instructor-generated material, such as example
solutions and lectures, as represented in the composite map
“Look/listen,” Fig. 6. The lectures were useful to suggest to
students both how they should and how they should not work
on problems.
Most instructors thought students could learn from instructor solutions, without working the problem first, if they
looked for an underlying structure in the solution and reflected on the solution.
“It’s a craft that students are learning. They’re not
learning momentum as a vector quantity that happens
to be conserved. They’re learning how to recognize
where that particular principle comes in a problem out
of the blue … learning the craft is not a matter of doing
10 or 50 or 100 or a million problems, in particular
following along somebody’s scanned solution, and decide that you know the physics. The learning the craft
occurs in little jumps along the way when you suddenly say, ‘oh that’s what this angular momentum is all
about, ok, I now have mastered the idea of it.” 关I4, 9,
14, 25兴
As with any craft, it was important that the students practice
applying concepts and processes for themselves.
020109-12
“They have to explore what that tool can do for you…
It’s important to explore for yourself what you can do
with physics ideas or formulas.” 关I1, 105, 295兴
PHYSICS FACULTY BELIEFS AND… . I. …
PHYS. REV. ST PHYS. EDUC. RES. 3, 020109 共2007兲
FIG. 6. 共Color兲 “Look/Listen” composite map of faculty beliefs about learning from looking at or listening to an instructor’s lecture or
example problem solution. Numbers in the parentheses denote the instructor whose statements directly justify that category. The boxes
framed with a double line indicate principal categories that are elaborated in other composite maps.
D. What prerequisite knowledge and skills do instructors
expect of their students?
Student characteristics that instructors believed were required for success in their introductory physics course are
shown in the composite map “Students Who Can Improve,”
Fig. 7. The prominent location of the box “Students Who
Can Improve” on the main map reflects the importance the
instructors gave to this issue. Early in the interview half of
the instructors described, without prompting, their class composition and to which part of it they direct their teaching.
This issue was also discussed in response to a question posed
near the end of the interview regarding the difference between students that were able to improve and those who did
not. Looking at this composite map one can see that most
instructors believed the class was composed of three groups:
共1兲 Students who are not going to learn how to solve
physics problems 共15%–33% of the course population兲.
“There are people that are just not ever going to be
able to do math properly.” 关I6, 312兴
共2兲 Those who are so good they do not really need the
course 共a few percent of the course population兲.
“There are a few, but very few, students who can basically bullshit their way through their introductory
physics, chemistry, and math classes, and basically get
good grades by doing nothing.” 关I5, 377兴
They work in an idiosyncratic way.
“They break all my rules and get away with it because
they are right… and they know what they were doing.”
关I3, 231兴
共3兲 The third group of students that can learn how to solve
physics problems 共but do not necessarily do so兲.
“I think you always have to pick out the middle ones
that are almost there or about there, to be able to get
them over the hump.” 关I6, 30兴
Every student in the third group was intelligent enough to
succeed in the course:
“Most of the students in our calculus-based physics
class are pretty bright.” 关I5, 391兴
Yet, not all would succeed. Their success was primarily de-
020109-13
PHYS. REV. ST PHYS. EDUC. RES. 3, 020109 共2007兲
YERUSHALMI et al.
FIG. 7. 共Color兲 “Students Who Can Improve” composite map of faculty beliefs about students who can improve meaningfully in their
introductory physics course. Numbers in the parentheses denote the instructor whose statements directly justify that category. The boxes
framed with a double line indicate principal categories that are elaborated in other composite maps.
termined by the following personal characteristics:
共a兲 Willingness to work hard on the course material. All
instructors thought that this was required to succeed in the
course.
“Some of the students actually collapse from the shock
of actually having to put in time in college courses.
That’s another way they can go down… Some of it
depends on how hungry they are, you know, how much
are they willing to put themselves out for this.” 关I5,
394, 399兴
why I wrote this particular line of algebra down.” 关I4,
c419兴
Using reflective study habits includes being able to interact with others.
“Being outgoing so they can talk to either their classmates or us, teaching staff.” 关I1, 363兴
共d兲 Possessing beliefs about their learning as an active
process in contrast to most students.
“Students come to lecture, read the newspaper, enjoy
the lecture, watch the demonstrations, watch me go
through the examples, and then they go and do other
things for the rest of the day; until a quiz, and then in
the days before a quiz they read the chapter and they
think about some problems.” 关I2, 29兴
共b兲 Caring about the course, being internally motivated.
“Interest, whether it be purely due to grades or not, can
make a difference between students who are able to
make improvements and students who are not” 关I1,
360兴, “the people that enjoy a challenge.” 关I6, 299兴
共e兲 Having self-confidence.
共c兲 Having reflective study habits.
“I think it goes back to the how you learn physics. You
have to, you look at problems not to go through the
problem and compare your answer with the one that’s
in the back of the book or up on the blackboard. But
instead you have to discipline yourself to say what,
why did I write this down. Exactly what was the reason
“If they perceive themselves as not good at things, then
they’re not willing to spend the effort on it.” 关I6, 315兴
The instructors’ believed that only some of the students possess these necessary characteristics because of a variety of
factors:
“I wouldn’t discount just the native skills and intelli020109-14
PHYSICS FACULTY BELIEFS AND… . I. …
PHYS. REV. ST PHYS. EDUC. RES. 3, 020109 共2007兲
gence from genetics or early background.” 关I6, 313兴
They thought many of these students do not seriously try
working a problem before looking at the solution.
“The student who’s all haggard and tired from jobs”
关I4, 399兴.“My guess is that the students have been
taught plug and chug physics in high school…We need
to work on distressing things, but in some sense the
best way to avoid bad habits is never to establish them
in the first place.” 关I3, 2-3兴
“When students do homework or solve problems, it’s
so tempting to just look at solutions after working
2 minutes if you don’t know what to do.” 关I1, 140兴
Regarding student use of the instructor solutions they
said:
“Success in education depends on previous socialization.” 关I5, 398兴
At no time did any of the instructors express the belief that it
was their responsibility to help students develop these beneficial characteristics. At most they hope to motivate those
they can.
“There are many students who make a mistake on the
quiz and say “well that was a mistake” and then
they’re not interested in it anymore.” 关I2, 26兴
They thought even when students looked at instructor solutions they did not focus on the physics of a problem.
“Unfortunately, there is a big gap between what I
would like students to do with solutions that I post and
what I’m fairly sure they are doing with them… The
majority of the students actually don’t look at the solution that I post… A large fraction of students who do
look at my solutions are focusing too much on the very
problem at hand 共‘what is the speed or how high will it
go’兲 as opposed to the structure of the problem.” 关I3,
31-33, 38兴
“If I can interest 20-30% of the class… then I’m being
successful.” 关I2, 36兴
E. How do instructors characterize their students’ actual
learning practices ?
In all parts of the interview, the instructors described their
typical students’ skills, attitudes, and behavior, which were
related to learning how to solve physics problems as well as
to general learning. The composite map “Typical Students”
has two parts: Fig. 8 presents students’ knowledge and skills
related to problem solving and Fig. 9 presents students’ characteristics related to general learning.
Student problem-solving skills were considered from several perspectives. Their knowledge of physics concepts was
described by all instructors as poor, as was their approach to
solving a problem and their ability to reflect on their solution
process.
“When I do solutions on the board during class I hope
that students just see how a professional thinks about
these sorts of things. Of course I suspect in many cases
they adopt the superficiality of it rather than thinking
of the details.” 关I6, 20兴
The instructors thought that students believe learning
physics is about technical skills and easier than it is.
“Techniques is probably the only thing many of the
students think there is to physics.” 关I1, 345兴
“Students often do not know what things would work
when solving an introductory physics problem.” 关I1,
33兴
“There are more students who think they can get good
grades by doing nothing, than those who can actually
do it.” 关I5, 379兴
“Everybody looks up formulas at some level. But relying on that as an alternative to understanding things is
the problem there.” 关I6, 259兴
They considered students’ motivation to be grade oriented:
“Students are seeking as high a grade as possible” 关I4, 123兴.
Most of the statements about student learning characteristics
were judgmental, and the instructors were much more detailed about negative aspects of students than positive ones.
To summarize, the instructors believed that their typical
student had seriously deficient problem-solving skills, general learning skills, beliefs about the goals of a physics
course, and motivation. The only skills that instructors mentioned in a positive way were that some students formed
study groups or were able to perform specific problem- solving techniques such as drawing free body diagrams.
Nevertheless, all of the instructors believed that the majority of their students did learn in their course. In most
categories that they defined as “Appropriate Knowledge”
共PHYSICS CONCEPTS, APPROACH TO SOLVING A
PROBLEM, and SPECIFIC TECHNIQUES兲, the instructors
estimated that their typical students were anywhere between
“some” to “a lot” better after the course. Instructors were
much less optimistic about the category of SELF EVALUATION. They expected that this type of reflection while solving a problem is something that takes more time to develop
“I suspect it’s very difficult for students to sort of step
back and be able to have the sort of oversight.” 关I1, 56兴
The instructors thought that students believe problem
solving should be quick and straightforward.
“Perhaps it’s unfortunate but students kind of want the
quick and dirty deal here” 关I6, 51兴, “to get to the answer in one shot.” 关I1, 115兴
Finally, students’ communication was considered as poor
because students
“don’t write solutions that someone else can understand.” 关I3, 54兴
The description of the typical student focused on the lack of
problem-solving skills or negative attitudes and behaviors.
All instructors thought that the typical student had behavior patterns that were not conducive to learning from working problems and getting feedback about problem solving.
020109-15
PHYS. REV. ST PHYS. EDUC. RES. 3, 020109 共2007兲
YERUSHALMI et al.
FIG. 8. 共Color兲 Part of composite map “Typical Students” concerned with faculty beliefs about the knowledge and skills related to
problem solving of typical students in their introductory physics course. Numbers in the parentheses denote the instructor whose statements
directly justify that category. Uppercase labels refer to specific types of knowledge that also occur in the “Appropriate Knowledge”
composite map shown in Fig. 3.
and should not be expected of students after a single yearlong class.
“The types of things in this stack 共named MATURITY,
containing. ⬘Have faith in answer’, ‘Recognize when
something is missing’, and ‘Comment on result’兲 are
not built up over one course… I hope they learn some
of it in the course, but it’s not, these are things that
aren’t in the syllabus and that you hope over 4 years of
a university education, that they cultivate.” 关I3, 373兴
most students did not have such skills when entering their
course, nor did they develop such skills in their course.
F. What values underlie how instructors would prefer to design
their instruction?
It is important to emphasize that this last category was
comprised of skills that instructors believed would be a prerequisite for a student to learn from attempting to solve problems in the course. But at the same time, they believed that
When discussing the instructional artifacts, the instructors
often expressed some conflict about how they believed they
actually designed their instruction as opposed to how they
would prefer to design their instruction in the absence of all
perceived constraints. There appeared to be four different
instructor values, given below, that underlie their beliefs
about how they would prefer to design their instruction of
introductory physics. These values appear in the composite
020109-16
PHYSICS FACULTY BELIEFS AND… . I. …
PHYS. REV. ST PHYS. EDUC. RES. 3, 020109 共2007兲
FIG. 9. 共Color兲 Part of composite map “Typical Students” concerned with faculty beliefs about characteristics related to the general
learning of typical students in their introductory physics course. Numbers in the parentheses denote the instructor whose statements directly
justify that category.
maps related to instructional resources such as problems, individualized feedback, and example problems solutions. For
example, Fig. 10 shows the values part of the composite map
“Appropriate Problems,” dealing with instructors’ beliefs
about the appropriate structure of problems. 共The rest of this
map deals with instructors’ beliefs about matching problems
to perceived constraints, and will be discussed in the next
section.兲 In the same way Fig. 11 shows the values part of
the composite map “Appropriate Example Solutions,” and
Fig. 12 shows the values part of the composite map “Individualized Responses.” 共See the Auxiliary Appendix of the
companion paper 关58兴 for the problem and solutions referred
to in the statements below.兲
“So that’s a nice set of questions which requires the
students to think about the physics principles behind
this problem.” 关I2, 249兴
Every feature of the problem should serve to add conceptual
challenge.
“I’m not sure that the context in problem C adds that
much to the problem.” 关I3, 286兴
Numerical grading was perceived as a tool to allow students to know what is missing in their solution, to encourage
students to do the correct things in a solution, and discourage
the incorrect.
1. Value 1. Instructors value engaging students in proper
physics practice which uses correct and efficient implementation
of fundamental physics concepts to solve physics problems
All the instructors thought that problems should be designed to involve students in determining which principles
and concepts should be applied to solving the problem.
020109-17
“Getting graded tests or quizzes back is basically a
one-line feedback to students about where they are. By
looking at their test score a student gets some feedback
about whether they’re missing something, or it’s OK,
or it’s a disaster, or whatever.” 关I1, 129, 134兴
PHYS. REV. ST PHYS. EDUC. RES. 3, 020109 共2007兲
YERUSHALMI et al.
FIG. 10. 共Color兲 Values part of composite map “Appropriate Problems” concerned with faculty beliefs about the appropriate structure of
problems in their introductory physics course. Numbers in the parentheses denote the instructor whose statements directly justify that
category. The boxes framed with a double line indicate principal categories that are elaborated in other composite maps.
Three instructors thought their example solutions should
be in a form that an expert physicist would write when doing
physics.
2. Value 2. Instructors value conveying the message of the
beauty of physics and the satisfaction they find in it, which
requires clear communication, relevance to reality,
freedom of thought, and ego fulfillment
“I post Instructor Solutions to demonstrate what a professional physicist strategy for the problem solving
would be.” 关I6, 12兴
Instructors’ appreciation of the clear and efficient style of
communication of physicists was reflected in statements
about how they design problems.
It should be an effective solution—the shortest path to arrive
at the result.
“I think we should be as clear in stating a test problem
as I think my graduate students should be when talking
to me about what they are working on.” 关I3, 295兴
“Instructor Solution 2 关is poor because it兴 goes through
step by step instead of simply writing down the important parameters.” 关I2, 51, 76兴
“I don’t like problem B because it is awfully wordy.”
关I2, 238兴
It should not give the implicit thought process, and it should
avoid giving generalizations or pointing out possible complications for the sake of being compact.
They wanted to include realistic context in a problem to
convey a message that physics is real and relevant, and they
rejected problem contexts that they did not believe could
actually take place.
“When I am solving a problem I don’t say to myself
out loud or even quietly all of the explicit things 共‘that
first I need to find this, then I need to do that’兲 as
Instructor Solution 2 does.” 关I2, 54-5兴
“Problem A will give them the impression that physics
is completely isolated from real life.” 关I1, 254兴
“Context rich problems are better if they really correspond to some situation that’s real, that’s really real
rather than sort of a contrived situation.” 关I4, 308兴
“The possibility of a lot of complications is allowed in
Instructor Solution 2 and they’re tossed out. A more
expert solution 共like Instructor Solution 1兲 doesn’t
even mention that term in the first place… I’d prefer to
see a problem solving approach in an instructor solution that more artfully tailors the solution to that particular problem rather than having some more general
approach.” 关I4, 48, 58兴
“Problem C is not really real life because, in reality,
nobody is going to throw a bag of nails up on a roof by
twirling it on the end of a string. Most people are going
to use a hoist or a man-lift, or something like that…A
real-life problem must have situations where, for example, architects and structural engineers would actually deal with.” 关I5, 245, 250兴
020109-18
PHYSICS FACULTY BELIEFS AND… . I. …
PHYS. REV. ST PHYS. EDUC. RES. 3, 020109 共2007兲
FIG. 11. 共Color兲 Values part of composite map “Appropriate Example Solutions” concerned with faculty beliefs about the appropriate
structure of example solutions in their introductory physics course. Numbers in the parentheses denote the instructor whose statements
directly justify that category.
They thought that instructor example solutions should
emphasize the message of individual creativity.
“To say to the student ‘Oh, but you have to go through
these individual steps which are implicit in the solution
that you‘ve already gotten,’ that ‘it doesn‘t count,’ or
that ‘we want you to approach this solution by analyzing each step, and then assembling those steps into a
final solution,’ that is asking the student to take a particular approach to solving the problem.” 关I2, 79兴
The reason to change policy was that taking off points might
discourage able students.
“I would want to see Student Solution E not discouraged by grading them harshly even if you had the
policy of, display your work, because, it’s a student
expert in my opinion.” 关I4, 170兴
“This sounds very elitist, but letting the good students
know that they‘re good at physics … .” 关I3, 405兴
“I think having a lot of writing 共like Instructor Solution
2兲 has the effect of saying ‘I want to have a kind of a
standard way to do 2-dimensional motion
problems…Solving physics problems is kind of an art,
It’s not exactly something that you just follow some set
path and crunch your way through to a solution.’” 关I4,
51 56-7兴
Most of the instructors could not believe that the student
who wrote Solution E could have made the same physics
errors as the student who wrote Solution D, even though the
two solutions were identical except that student D wrote explanations while student E did not.
Finally, instructors wanted to make sure numerical grading provided ego gratification to the good student. The instructors raised this issue when they discussed Student Solution E 共a very sparse solution with a correct final answer兲
because their inclination was to violate their grading policy
of requiring justification of the final result.66 关The student
artifacts can be found in the companion paper 共Ref. 58兲.兴
“Yeah, I do have the policy that students have to explain their work.” 关I4, 171兴
They recognized that Student Solution E is missing reasoning.
“Student Solution E certainly doesn’t give you much in
the way of explanation for the solution.” 关I6, 102兴
what’s going on.” 关I3, 228兴
3. Value 3. Instructors value helping student learn by presenting
students explicitly with what they should know
Instructors value presenting students with all that they
need to know to determine the answer to a problem. This
value is reflected in three instructional actions: 共1兲 supplying
problems broken down into small subparts so that students
are led to solve the problem efficiently; 共2兲 modeling how a
student, who did not know how to solve a problem could
approach it and then communicate the solution; and 共3兲 providing the students with a diagnosis of the nature of deficiencies in their solutions.
Several instructors were aware that the artifact Problem A
walks the student through the solution process, in comparison to the version of the problem they received ahead of the
interview as “homework.”
“Instead of throwing the students a compound problem
written in a way like the 1homework’ and expect them
to be able to divide it into parts, alternatively, you can
present the same problem already divided into parts
Yet, they decided to ignore it.
“There is a switch that I turn on when I’m dealing with
a student 共like Student Solution E兲 who I think knows
020109-19
PHYS. REV. ST PHYS. EDUC. RES. 3, 020109 共2007兲
YERUSHALMI et al.
FIG. 12. 共Color兲 Values part of composite map “Individualized Response” concerned with faculty beliefs about the appropriate structure
of individualized response in their introductory physics course. Numbers in the parentheses denote the instructor whose statements directly
justify that category.
and attempt to lead the students through it.” 关I5, 218兴
“The strategic things that students should get out of
instructor solution’s include the ability to translate the
problem into a physical diagram of the situation, identify exactly what’s being asked, identify what fundamental physics concepts are going to be used to solve
the problem, and to determine a sophisticated and disciplined path to solve the problem.” 关I3, 50兴
Some thought it is a good thing.
“You’re giving students a chance to show that they
know kinematics and then that they know energy conservation and then finally that they know about rotational dynamics.” 关I3, 319兴
“It does guide students to doing it the right way.” 关I6,
174兴
Others disliked Problem A, either because guiding the student does not respect their individual freedom of thought, or
because it does not guide them the right way.
“Problem A leads the students in the wrong direction at
first, which I think is perverse.” 关I5, 263兴
The instructors believed that modeling a solution should
reveal the underlying approach to solving a problem. The
student should get the nature of the problem-solving process,
either the linear nature or the exploratory nature, depending
on the instructor’s view of the problem-solving process.
“In my instructor solution I try to emphasize when the
solution is not logical and when I guessed and used
trial and error by saying that ’I noticed that this relation might work.’ ” 关I1, 31兴
Finally, instructors valued explaining to students where
they went wrong.
“Obviously if you find that there’s just some misperception displayed in some student’s solution to a problem, if the grader can say, ‘does not apply here
because…’ or something like that, it’s certainly very
useful to the student.” 关I4, 132兴
Even numerical grading was perceived as a tool to show
020109-20
PHYSICS FACULTY BELIEFS AND… . I. …
PHYS. REV. ST PHYS. EDUC. RES. 3, 020109 共2007兲
students what thought processes are missing from their solution, to encourage appropriate approaches, and to discourage
the inappropriate ones.
“When a student gets too much help when solving
problems they get away without actually thinking on
their own.” 关I1, 322兴
“I tend to look at grading a test as almost an essay
rather than multiple choice. I want to see the reasoning.” 关I6, 79兴
“I almost never give straight problem solutions during
lecture—I have students list the target quantities, list
the so-called known quantities, and what kinds of relations they think they can use to relate them.” 关I1, 38兴
“I do try and design my grading, my feedback mechanisms, to specifically discourage things that I think are
very bad habits, for example not awarding partial
credit in cases where a solution paper sort of carpet
bombed the formulas.” 关I3, 370兴
Most often guiding students in this way was in the context of
coaching a student in their office.
“When you send a student to the blackboard and quiz
them, in the worst case, they’re going to say, ⬘I haven’t
any idea what to do in this problem, I’m just absolutely
in the dark.’ So you say, ⬘All right, let’s start’… What
do you think happens? Draw a picture of what you
think happens.” 关I4, 329兴
“I have told my TA’s that if the student writes something indicating PERSPECTIVE that they should get
credit for it.” 关I2, 293兴
“I kind of try to probe, well, what are you thinking.”
关I6, 245兴
4. Value 4. Instructors value helping students learn by having
students find their own path to a solution
Several instructors stated that they designed problems to
challenge students and have them explore the possible solutions. For this reason, one instructor believed he should not
break down problems into smaller subproblems.
The instructors tend to call this mode of teaching “Socratic
dialogue” 关I3, 43兴. Four instructors mentioned group work as
a venue to encourage students to reflect on their problem
solving.
“I think mixed gender study groups are more effective
in helping students learn because, particularly first year
male students, half of them are not capable of studying
in all-male groups and getting an optimal return out of
that, because they’re too much into not admitting that
they don’t know something.” 关I5, 385兴
“I stopped using problems like Problem A because they
give too many hints, which I want students to be able
to figure out on their own.” 关I3, 252兴
Several thought they should pose conceptual challenges to
their students.
“These 共parts of Problem D兲 are great with the acceleration. Students are going to be scratching their heads
for a while.” 关I3, 337兴
Several instructors hoped students would reflect on their solution by requiring them to verify their answers, for example
by multiple-choice problems.
“If you had definite answers 共as in Problem B兲 it might
make you check back your answer.” 关I6, 223兴
One instructor insisted that in his example solution he would
not show the underlying reasoning as it denies students the
opportunity to figure things out by themselves.
“With an instructor solution like Instructor Solution 1,
some students will do a lot of figuring out. That process is probably useful.” 关I1, 80兴
All instructors believed that learning takes place when students explicitly employ metacognitive processes while solving problems and that they could guide students to do this.
“I guess coaching them to always go back to the big
picture technique 共Where are you? Have you figured
out all the physics parts? Have you understood the English? Have you understood the physics?兲 would help
students in this area.” 关I1, 318兴
Four instructors explained how they would guide a student to
reflect on their problem solving by limiting direct support
while probing the student.
In summary, values 1 and 2 共engaging students in proper
physics practice and conveying the message of the attractiveness of physics兲 seem to reflect the faculty perception of the
physics culture because they focus on how physicists solve
problems and what they enjoy when practicing physics. Values 3 and 4 共helping students learn by explicit guidance or by
having students find their own path兲 seem to reflect the faculty perception of a teaching culture because they focus on
how a teacher mediates the subject matter to the student.
Values 3 and 4 imply two contradictory learning/teaching
models. The first is transmitting: providing an explicit path
for the student lacking that knowledge. The second is extreme constructivist: setting goals without limiting student
options. The same instructors expressed these different and
sometimes conflicting values in different parts of the interview. No instructor explained how they might integrate these
values or seemed aware of the conflicts.
G. What instructors believe limits their instruction
As mentioned earlier, all of the instructors believed that at
least three constraints caused them to compromise their instruction: 共1兲 their workload and that of their teaching assistants, 共2兲 students’ expectations and preferences, and 共3兲 their
limited professional knowledge. These constraints appear in
the composite maps related to the instructional resources.
Figure 13 shows the constraints part of the “Appropriate
Problems” map 共completing the partial map of Fig. 10兲. Figure 14 shows the constraints part of the “Appropriate Ex-
020109-21
PHYS. REV. ST PHYS. EDUC. RES. 3, 020109 共2007兲
YERUSHALMI et al.
FIG. 13. 共Color兲 Constraints part of composite map “Appropriate Problems” concerned with faculty beliefs about the appropriate
structure of problems in their introductory physics course. Numbers in the parentheses denote the instructor whose statements directly justify
that category.
ample Solutions” map 共completing the partial map of Fig.
11兲. Figure 15 shows the constraints part of the “Individualized Responses” map 共completing the partial map of Fig.
12兲.
bor intensive, and we’re always kind of short of man or
person-hours to do everything that needs to be done
with the elementary teaching.” 关I4, 130兴
They also recognized that they can do very little coaching.
1. Constraint 1. Workload
“Well it’s, obviously in a big lecture it’s impossible to
do.” 关I1, 326兴
The limited time instructors could afford to put into their
courses affected how they designed both the tasks and the
feedback for their students. Half said that they give multiplechoice problems mainly to make grading easier.
“I use multiple choice questions 共like Problem B兲
partly to go easy on the TA’s.” 关I2, 236兴
Four instructors believed that writing problems that focus
on qualitative features requires too much time.
“I think engaging students and getting them to do
something, no matter how wrong it might be, getting to
do something on their own while you help them is, I
think, the key. It’s labor intensive though.” 关I4, 339兴
They thought that even the limited time they can provide is
not appropriately used by students.
“One thing I was disappointed with in that course, and
in others, is figuring out ways of getting students involved with coming to office hours and things like
that.” 关I6, 338兴
“It would be, yeah, I would do stuff like this 共Problem
D兲 to the extent that I have time to do the graphics.
This is labor intensive.” 关I4, 300兴
All instructors thought that instructor solutions should require a minimum amount of instructor time.
“If I can find a solution worked out, then I can scan it
and put it on the web. To do more than that, more
complex solutions, would take much longer, and I
don’t have the time, so I use solutions like instructor
solution 1.” 关I5, 44, 46兴
2. Constraint 2. Students’ expectations
Instructors recognized they do not provide as many diagnostic comments as they favored.
“Making useful comments on the quiz solutions is la-
When considering time constraints, the instructors focused
on their time outside of the classroom used to prepare resources, grade, or coach. Shortage of time in the classroom
to “cover the material,” often expressed by faculty,67,68 did
not arise as a constraint in any interview.
This constraint had three manifestations. The first is not
requiring actions that instructors believe add too much stress
to the student.
020109-22
PHYSICS FACULTY BELIEFS AND… . I. …
PHYS. REV. ST PHYS. EDUC. RES. 3, 020109 共2007兲
FIG. 14. 共Color兲 Constraints part of composite map “Appropriate Example Solutions” concerned with faculty beliefs about the appropriate structure of example solutions in their introductory physics course. Numbers in the parentheses denote the instructor whose statements
directly justify that category.
“I don’t like it 共Problem C兲 as a test problem in a
high-pressure situation.” 关I3, 284兴
3. Constraint 3. Professional knowledge
Instructors recognized that certain instructional actions require them to think about students’ difficulties in a way that
is not natural for them.
“Now let’s see. Is Problem A stated in such a way that
it gives an easy analysis?” 关I4, 269兴
“If I were preparing a solution sheet and posting a
solution sheet, my tendency would be to simply post
this 共Instructor Solution 1兲, because I don’t anymore
discipline myself to say that a problem solution has to
be done in the various steps that are implicit in IS
共Instructor Solution兲 2.” 关I2, 68兴
All instructors thought that instructor solutions should not
be too long or complicated in order not to repel students.
“There is a class of students who will get this problem,
walk right through it, without worrying about this
point. So they might be thrown a little by putting this
description 关of possible approaches兴 in the middle of
Instructor Solution 3.” 关I3, 119兴
“It takes a lot of work to write a multiple choice question. In this case you have to go through the possible
ways that people can go wrong.” 关I3, 277兴
“Explicit details—is I think it kind of turns students off
in some ways… You look at Instructor Solution 1 and
say ‘oh, that’s a nice easy problem’ and you look at
Instructor Solution 2 and say ‘oh gosh, this is really
complicated.’ ” 关I6, 52, 54兴
“Even though I like Instructor Solution 3 I’m likely to
produce something like Instructor Solution 1 because
I’m not very good at spelling things out in this way. I
have a tendency to race ahead because I see my way
through to the end.” 关I4, 93兴
The final students’ expectation constraint was avoiding a
confrontation with students, especially the good students.
“If I had graded this not very well and the student
came back to me and says, ‘but I got it right,’ that’s
what I would tell them, is that you didn’t really show
that you’re doing the right principles… I would tend
more to give them the benefit of the doubt when grading a quiz solution.” 关I6, 133, 143兴
One instructor recognized that he lacks the knowledge for
constructing problems that will cause student solutions allowing him to provide feedback on issues he deems important.
“… providing positive feedback to encourage the types
of things… There’s nothing specifically that we test for
020109-23
PHYS. REV. ST PHYS. EDUC. RES. 3, 020109 共2007兲
YERUSHALMI et al.
FIG. 15. 共Color兲 Constraints part of composite map “Individualized response” concerned with faculty beliefs about the appropriate
structure of individualized response in their introductory physics course. Numbers in the parentheses denote the instructor whose statements
directly justify that category.
that really brings these things out.” 关I3, 372兴
Another instructor noted how norms change and with them
instructors’ awareness of the need to communicate reasoning.
“Now, if we were doing this the way we, you know, I
think everybody is making more of an emphasis about
explaining your work, we do that a good deal more.
Years back we didn’t. We said, ok, answer. So by the
old method of grading Student Solution E would be a
10. No problem.” 关I4, 168-9兴
Because these perceived limiting factors often conflict with
an instructor’s values, their instructional preferences reflect
how they resolve this internal conflict.
ing the teaching culture 共values 3 and 4兲, the instructors’
preferences tend to align most closely with the physicist culture. For example, instructors described their problem solutions, both in the classroom and as posted solutions, as being
similar to Instructor Solution 1. This solution presents a compact path to arrive at a correct result, reflecting the concise
communication physicists appreciate. They did not believe
they should provide detailed solutions because of their belief
that such solutions limit the students’ intellectual freedom of
having their own solution style.
Those instructors who favored giving solutions that detailed the underlying thought process felt constrained not to
do so because of lack of time or lack of knowledge of how to
do so. They recognize that students have difficulty understanding their short expert solutions.
“A student who was not able to do the problem might
find an instructor solution that is just symbols equally
foggy, equally unclear.” 关I2, 73兴
H. How do instructors weigh their values, perceived
constraints, and beliefs about students to arrive at their
instructional preferences?
The instructors often expressed that they were conflicted
about their instruction.
However their response is to supplement their actions in a
manner which is not totally satisfactory to them.
“In the ideal world you would use problem solutions
and grading of them far more for teaching than for
stratifying the student population. But I think the real
situation here, and probably it’s typical, is that you just
don’t have the time for it.” 关I4, 133兴
“What I do when a student comes to me and says ⬘I’m
having trouble’ is to give him another
textbook…Which for many students is enough, but for
some students, it doesn’t turn out to be enough, or for
some students it doesn’t speak to the way they think.”
关I2, 298兴
When faced with internal conflicts between values reflecting the physicist culture 共values 1 and 2兲 and values reflect-
The problems instructors described assigning their students tended to be stripped to the essential physics and effi-
020109-24
PHYSICS FACULTY BELIEFS AND… . I. …
PHYS. REV. ST PHYS. EDUC. RES. 3, 020109 共2007兲
ciently communicated. A minimal context was often used to
communicate their value of physics representing reality, but
the context was perceived as being stressful to the student.
Many features of instructional design that were believed to
be useful were not used because the instructors perceived
them as not being necessary components of physics knowledge. For example, although they believed having a problem
context raises student motivation and reflects the instructor’s
value of connecting physics to reality, they chose not to provide problem contexts. Instructors perceived adding context
to problems as assessing language skills, which they did not
see as appropriate.
“I feel very reluctant to put anyone in a situation where
their ability to parse an English sentence has a significant impact on their grade.” 关I3, 302兴
Instructors also believed that effective learning of physics
using problem solving required students to construct their
own solution path to a realistic problem. However, they had
difficulty conceiving how to assess such student action when
it did not result in a correct answer or how to give feedback
to encourage it. Their resolution was to give such problems
in nongraded situations.
“Maybe more for a homework problem that would be
all right or for a group problem in a discussion section
for example.” 关I6, 187兴
Their feedback on students’ work consisted primarily of
numerical grading that penalized clearly incorrect
statements.66 Instructors took special care in grading to bolster the self-esteem of the students they judged as good.
Feedback about reasoning was valued only for those students
they judged as poor, although few expressed the ability to do
this due to time constraints. Coaching students was primarily
discussed with respect to their individual actions with the
few students who came to their office hours. Some mentioned the value of peer coaching of students working in
groups. However, even though all instructors had many
teaching assistants whose primary function was to coach students, none mentioned managing this TA resource as a way
of giving guidance to the students.
When matching their conflicting teacher values to their
preferred actions, the result appeared to be an unstable set of
instructional beliefs. Sometimes the dominating value was
the desire to offer the students guidance 共Value 3兲, while
sometimes the desire was to have students figure things out
on their own 共Value 4兲. For example, several of the instructors were reluctant to write detailed student solutions that
would limit the student creativity that they valued, but favored breaking down a problem into parts to force a student
along an effective solution path.
A possible explanation for why instructors tended to give
their physicist values added weight is that they believed that
perceived constraints favor their physicist values. Their
physicist values are aligned to student expectations even
when they are not aligned with student needs, and tend to
minimize the perceived workload on the instructor and the
student and avoid professional skills that instructors believe
they lack.
VI. CONCLUSIONS
The most important conclusion of this study is that it appears to be possible to build a model of common faculty
beliefs and values with respect to the teaching and learning
of problem solving in introductory physics. The physics faculty that we interviewed appeared to have a limited and classifiable belief system in this domain. In the remainder of this
section we will first compare faculty views of teaching and
learning to instructional paradigms found in the research literature. We will then discuss implications for further research needed to verify and extend our initial model. Finally,
we will discuss possible implications for curriculum and professional development that might arise from this line of research.
A. Comparison with three instructional paradigms
Farnham-Diggory identifies three paradigms that underlie
all instructional theory:16 behavior, development, and apprenticeship. Each is founded on assumptions about the difference between a novice and an expert and the key mechanism of transformation from novice to expert. These are
briefly explained below so that they can be compared with
the beliefs of the instructors in this study.
共1兲 Behavior: The difference between a novice and an
expert is quantitative—experts simply know more than novices. Instruction involves an expert breaking down the
knowledge or skills to be learned into a sequence of smaller
steps. The role of the students is to master each step by
practice and repetition. The role of the teacher is to present
each step, provide opportunities for students to practice, and
provide appropriate reinforcements to encourage success.
共2兲 Development: The difference between a novice and an
expert is qualitative—experts have different cognitive structures than novices. Learners actively construct their mental
models through a process of resolving the conflict between
their existing ideas of the world and discrepant new insights.
Instruction based on this theory involves probing students’
existing models, then creating activities that 共a兲 challenge
their models, 共b兲 help students build new models, and 共c兲
help students apply their new models to novel contexts. The
role of the students is to discover the discrepant events in
carefully sequenced curricular material. The role of the
teacher is to assure that students participate in activities that
lead to the desired discrepant events, and appreciate the
event as discrepant, and to help students build a new model
that is consistent with their experiences.
共3兲 Apprenticeship: The difference between a novice and
an expert is their culture of practice. The fundamental units
of instruction are meaningful, “whole” activities 共e.g., solving authentic problems兲, as opposed to decontextualized
skill-building or concept-building activities. The role of the
student is to engage in activities that simulate those of the
field they are learning. During these activities, they interact
with their peers and with their instructor to reflect on the
connection between their existing experiences and ideas and
the ideas and procedures that more closely characterize the
field. The role of the teacher is to 共a兲 model explicitly the
intellectual skills and processes of the discipline, 共b兲 coach
020109-25
PHYS. REV. ST PHYS. EDUC. RES. 3, 020109 共2007兲
YERUSHALMI et al.
students while they use the procedures of the discipline to
engage in scaffolded, authentic activities, and 共c兲 gradually
decrease this support 共scaffolding兲 until students are independent.
The belief system of the instructors in this study regarding
the nature of expert knowledge and the nature of learning is
most closely aligned with cognitive apprenticeship. On the
other hand, their belief system regarding their role as a
teacher was not congruent with any of the three instructional
paradigms. This alignment is reflected in the following dimensions:
1. Nature of expert knowledge
Instructors perceive problem solving in physics as a central goal of the course. They believe the elements needed for
effective problem solving are the characteristics of the culture of physics, “how a professional thinks about these sorts
of things” 关I6, 20兴. They perceive expert knowledge as qualitatively different than that of the novice. They reject a view
of expert problem solving as an accumulated knowledge
built from an acquaintance with a large set of physics problems, although they recognize that this is the view of some of
their students.
“I’m afraid we have cases of students who… go and
look at the solutions and read them and say, ok now
I’ve read, or sort of gone through solutions for 50
problems, I know the physics”. 关I4, 20兴
In this sense, their vision of expert knowledge is similar to a
cognitive apprenticeship paradigm, namely that experts differ from novices in their intellectual context. Their goals for
student problem solving are consistent, to some extent, with
expert problem solving reported in the literature.60,69–73
These goals include students learning to:
共1兲 use effective problem solving approaches that consist
of an initial qualitative analysis of the problem, devising a
plan, and evaluating the plan. Some believe this approach
takes place in a linear process and others believe in an exploratory process that conforms more closely with the characterization of expert problem solving in the literature;
共2兲 demonstrate an understanding of physics concepts by
their correct use in problem solving;
共3兲 deploy specific physics and mathematics techniques
when appropriate;
共4兲 use self-evaluation both to guide the problem-solving
process and facilitate learning physics through problem solving; and
共5兲 appreciate problem solving as an intellectual
challenge.
Although the literature suggests that there are multiple
stages that characterize the journey from novice to expert74,75
and recognizes the necessity of establishing intermediate
goals for instructional purposes, these instructors had a dichotomist view regarding problem solving. They did not recognize any intermediate stages between expert and novice
problem solvers that might help guide their instruction.
2. Role of learner
The instructors believe their students learn to solve problems by watching an expert performance embodied in their
lectures and example problem solutions and by reflectively
attempting to work problems. It is this reflectivity that allows
students to use the teacher’s modeling and other feedback to
diagnose their own problem-solving deficiencies and remedy
them. According to the instructors, the primary role of the
learner is reflective: during the activity of problem solving
the student examines and expands upon their own ideas and
consciously generalizes and refines them. The instructors believed that this reflective approach was both a prerequisite to
effectively learn in their course and a desired outcome of the
course that was unattainable for most students. The instructors appear hostile to the behaviorist view of learning as a
process of individually mastering small steps that are predetermined by an expert and putting those steps together in a
predefined order.
3. Role of teacher
The instructors’ belief system contained several conflicting ideas about their role as teachers. Because different ideas
were activated in different contexts, the instructors were not
usually aware of the conflicts. They had internal conflicts
between their physicist values and their teacher values 共valuing compact solutions vs well-communicated reasoning兲 and
also within their teacher values 共strict guidance vs extreme
inquiry兲. Under the weight of perceived external constraints
共workload, students’ expectations, and limited professional
knowledge兲, those physicist values that emphasized product
over process tended to dominate teacher values that emphasized process.
The instructors’ ideas about the role of the teacher appeared to be an extreme form of constructivism coupled with
features of apprenticeship. In their view, the most important
aspect of learning takes place while a student works a problem. While engaged in solving this problem a student constructs their knowledge. The guiding principle of their teaching seemed to be modeling their own problem solving as an
example of expert problem solving without being explicit
enough to limit students’ freedom of thought or clash with
their expectations. Coaching was valued, but no scaffolding
should be used that constrains student actions and thus limits
their creativity. A Socratic-like dialogue with students that
supplies verbal scaffolding in office hours was not viewed as
a limit on student creativity. Most coaching was viewed as
giving feedback about student mistakes and allowing each
student to find their own way to a correct path. Some instructors accepted, with reservations, the scaffolding of dividing
problems into small, predefined subproblems, each of which
focused on a single concept or skill that the instructor perceived led to a solution.
There appeared to be a mismatch between the instructors’
view of student learning and their own actions in teaching.
While the instructors believed that reflective practice is essential for student learning and that most students in their
course were not reflective, they did not believe that they
should design scaffolding to help students develop that reflectivity. They were content with giving general suggestions
on how to approach learning and solve problems effectively.
This belief that they should not directly influence student
behavior occurred despite their very strong beliefs about the
020109-26
PHYSICS FACULTY BELIEFS AND… . I. …
PHYS. REV. ST PHYS. EDUC. RES. 3, 020109 共2007兲
need for student behavior to change in this domain. The instructors were not satisfied with how “the typical student”
engaged in learning activities. They pointed out student deficiencies similar to those reported in the educational literature. They believe that their students hold a naive view of
physics problem solving as “matching problems with facts or
equations and then substituting values”76 and that students
often believe that mathematical problem solving should be
quick and straightforward.59 They also believe that students
do not engage in the reflective learning activities60,76 and that
the students’ poor self-esteem can impede their ability to
learn in the course.77
Despite the instructors’ description of the typical student
as not having the required learning skills to achieve the goals
of their course, all of the instructors estimated that their students did learn between “some” and “a lot” in most categories that the instructors deemed to be appropriate knowledge
by the end of the course. The only exceptions were categories that specifically involved reflection, such as students understanding the process of problem solving or the use of that
understanding to evaluate their problem-solving process and
results. That students would develop some ability to reflect
on their problem solving was perceived as beyond the scope
of an introductory physics course. No instructor indicated an
awareness that this reflectivity, which at the end of the interview was judged to be too advanced for the course, was just
the collection of thought processes that they espoused as a
necessary condition for learning in the course.
B. Implication for further research
Based on our interviews of six professors from a single
research university, we have constructed a model of the beliefs and values of physics faculty with respect to teaching
problem solving within the context of introductory physics.
This model is part of the characterization of the initial state
of the instructor in a systems approach to changing instruction at universities and colleges. A knowledge of this initial
state is required to design the scaffolded professional development that could result in the desired final state of the instructor, the productive adaptation of research-based curricular material and pedagogy.
This model allows the formulation of testable hypotheses
that can and should be investigated by other means. Despite
the safeguards built into this study, any interview technique
has the possibility of contamination due to the interaction
with the interviewer. Additional biases arise from the interpretation of the statements in the interview and their categorization imposed by the investigators. For these reasons it is
important that independent investigators attempt to verify or
falsify the results. These results should also be tested for
their generality by similar interviews with a more diverse
population of physics faculty from the different types of institutions that comprise the higher education system in the
U.S. and other countries.
Because there is a close connection between the students
in university introductory physics and high school physics,
both in age of student and content of the course, we believe
researchers should investigate the linkage between these two
teaching contexts. Understanding the relationship between
high school and college teaching is crucial for an effective
education system because the high school teachers prepare
the students who populate the university courses and high
school teachers themselves are the direct product of the university. Of course, this type of study can also be used to
investigate instructor beliefs about other parts of physics
education such as establishing student knowledge about certain concepts. It can also be used to investigate instructors’
belief structure when teaching other subjects.
The hypotheses, represented by the categories and links of
the concepts maps presented in this paper, can be tested in
detail and those results used to modify the model. The existence of a specific instructor belief and its relationships to
their other beliefs about students, instructors, course content,
external constraints, or the intellectual and cultural values of
physics, represented by links on the concept maps, can be
investigated by more directed interview techniques or in a
statistical manner by the use of written questionnaires probing a limited domain of interest.
C. Implication for curriculum and professional development
It will take several years to achieve a detailed research
program that goes from this initial model to a robust map
representing the beliefs and values of a majority of physics
professors about the teaching and learning of problem solving in the context of introductory physics. In the following,
we use the initial model to formulate hypotheses to illustrate
how such a map might be used by those attempting to change
current pedagogy. We do not claim that this model has been
tested and elaborated sufficiently to actually use in this manner.
1. Identifying problems with professional development based on
attacking transmissionist beliefs about teaching and
learning
Our model implies that, although many physics instructors present their courses in a manner in which their goal
appears to be to transmit information to students, this is not
the case. Indeed, their unstated “learning theory” could be
characterized as extreme constructivist. Moreover, their beliefs about problem solving are very close to the accepted
views about the nature of expert knowledge and its differences with novice knowledge. Their pedagogical style does
not arise from a belief that students learn from clear explanations, a transmissionist learning theory. Instead it is the
result of a more complex interplay among their beliefs about
student learning, professional values, and perceived external
constraints. This hypothesis implies that instructors do not
need to be convinced that students must construct their own
knowledge. Introducing them to this research is not likely to
change their teaching because they already believe this is
true.
2. Designing new instructional materials
Our initial model indicates that physics instructors have
some dichotomous beliefs and many conflicting beliefs and
values about the learning and teaching of problem solving.
020109-27
PHYS. REV. ST PHYS. EDUC. RES. 3, 020109 共2007兲
YERUSHALMI et al.
This result is supported by similar, more general studies with
K–12 science teachers 共see Sec. II兲. This result also suggests
that a tested and revised model will not help curriculum developers design materials that would be accepted and used
by physics faculty without additional professional development.
For example, some of the faculty interviewed stated the
need for example problem solutions that make explicit the
expert thought processes in problem solving. They believed
that they had neither the time nor the professional knowledge
to construct such materials. This would seem to imply that
curricular materials designed to improve student problem
solving23,25,26,76 should supply a complete set of such solutions for the course. However, the explicitness of such solutions would violate the value of not constraining student creativity by giving an explicit trail of reasoning. It would also
violate the value of concise communication by explicitly describing reasoning processes that are typically implicit for an
expert. Finally it would violate the value of not undermining
student morale by making problem solving look too complicated. Thus one should not expect the availability of such
materials to lead to their acceptance or use.
Another example is providing activities in which it is necessary for students to use organized and well-communicated
problem solving to accomplish a task.78 Such a task might be
working in small collaborative groups to solve a realistic,
complex problem. This task requires coaching and other
scaffolding for most students to be successful. While instructors believe that reflective practice solving problems is essential for learning, they also believe that no scaffolding
should be used that constrains student actions and limits their
creativity. Instructors also do not recognize any intermediate
stages between novice and expert problem solving that might
help guide their instruction. Additional professional development would probably be required to strengthen an instructor’s belief in the need for scaffolding to help students become more expert-like problem solvers.
3. Designing short, one-time professional development
interventions
A knowledge of instructors’ beliefs and values can allow
curriculum developers to determine the alignment of their
materials with instructors. If the materials are reasonably
well aligned and do not conflict with any deeply held beliefs
or values, those instructors are potential adopters. A conventional dissemination strategy of short professional development workshops, designed to reinforce faculty conceptions
that align with the proposed materials while weakening undesirable beliefs by pointing out conceptual conflicts, could
be effective.
For example, in disseminating curricular materials in
which problem solving serves as a primary mode of learning
introductory physics,6–11 one might initially think that it
would be most important to focus on expert-novice differences in problem solving. An introduction to the results of
this research60 might be a useful introduction and prove reaffirming for faculty. However, it is already aligned with
their beliefs and thus is not likely to change their teaching.
With this knowledge, the professional development would
need to go further, perhaps focusing effort on introducing the
concept of scaffolding, as their beliefs have features of cognitive apprenticeship without the crucial idea of the use of
scaffolding. It is possible that exposure to models of cognitive apprenticeship instruction with an emphasis on the
building and eliminating of scaffolding would be close
enough to the instructors’ beliefs to be beneficial.
Short-term professional development could also explicitly
focus on exposing major inconsistencies in instructors’ complex belief structure. This could be accomplished by focusing on instructional materials that are known to cause conflicts. For example, we found that instructors have conflicts
about the role of context in problems and the consequences
of subdividing problems into parts. It might be beneficial for
an instructor to articulate their conflict while clarifying both
their values and perceived constraints that shape their instructional practice. At this point, instructors might be receptive to instructional strategies which resolve the conflicts using scaffolding techniques.
Professional development could also focus instructors on
other issues about which they are likely to have internal inconsistencies. For example, their perception of student learning matches their perception of useful instruction only if
their students are reflective learners, which they recognize is
not the case. One could build upon the similarity of their
beliefs regarding the nature of problem solving and learning
to research results by assisting them to articulate their goals
and their expectations of students entering their class. At the
same time, they could examine the characteristics of their
students so that they might recognize the gap between their
requirements for effective student learning and their actual
students’ characteristics. Once exposed, these inconsistencies
may provide instructors with motivation to engage in longterm professional development that allows them to become
familiar with techniques that resolve this conflict.
4. Designing long-term professional development
If new curricular materials violate key instructor beliefs or
values, one needs to design a thorough professional development to accompany and support a long-term process of a
fundamental cognitive change. This would require an intellectual environment that does not currently exist at most universities and colleges. The time required for such professional development would need to be made available to
instructors at the expense of one or more of their other duties. Research on in-service teacher education points out the
characteristics of professional development needed to
achieve such changes and encourage teachers to face the
risks and cope with the difficulties entailed in such a
transformation.79–81 As in any human change of deep-rooted
beliefs, the instructors will need to take an active role by
consciously reflecting on their beliefs and practices while
tailoring the innovations to their specific context.82–84 Such
changes would need a model of professional development
that is more extensive than a several hour or even several day
workshop. This model would probably need to be implemented while the instructors are in the process of teaching a
course and involve the modeling, coaching, and fading aspects of cognitive apprenticeship. Unless this time of exten-
020109-28
PHYSICS FACULTY BELIEFS AND… . I. …
PHYS. REV. ST PHYS. EDUC. RES. 3, 020109 共2007兲
sive and long-term professional development is envisioned
when the curricular material or pedagogy was designed, the
most effective action for change would probably be to develop materials that avoid this intellectual confrontation.
ACKNOWLEDGMENTS
Foundation Grant No. DUE-9972470 and the University of
Minnesota. Additional assistance was provided by the Weizmann Institute. We would like to thank the faculty and graduate students of the University of Minnesota who participated
in this study and the preliminary studies that led to the development of the interview procedure.
This study was partially funded by the National Science
*Previously at School of Physics and Astronomy, University of
Minnesota, Minneapolis, MN 55455, USA.
†
Present address: Department of Physics, Colorado School of
Mines, Golden, CO, 80401, USA.
1 K. Samuelowicz and J. D. Bain, Conceptions of teaching held by
academic teachers, J. Higher Educ. 24, 93 共1992兲.
2 M. Prosser and K. Trigwell, Understanding Learning and Teaching: The Experience in Higher Education 共St. Edmundsbury
Press, Great Britain, 1999兲.
3
C. Brass, R. F. Gunstone, and P. Fensham, Quality Learning of
Physics: Conceptions Held by High School and University
Teachers, Res. Sci. Educ. 33, 245 共2003兲.
4 C. Henderson and M. Dancy, in Proceedings (peer reviewed) of
the 2004 AAPT Physics Education Research Conference, edited
by S. Franklin, J. Marx, and P. Heron 共American Institute of
Physics, Melville, NY, 2005兲.
5 A. G. Thompson, in Handbook of Research on Mathematics
Teaching and Learning, edited by D. A. Grouws 共MacMillan,
New York, 1992兲, p. 127.
6 J. P. Mestre, R. J. Dufrense, W. J. Gerace et al., Promoting skilled
problem-solving behavior among beginning physics students, J.
Res. Sci. Teach. 30, 303 共1993兲.
7 A. Van Heuvelen, Learning to think like a physicist: A review of
research based instructional strategies, Am. J. Phys. 59, 891
共1991兲.
8 P. Heller and M. Hollabaugh, Teaching problem solving through
cooperative grouping. Part 2: Designing problems and structuring groups, Am. J. Phys. 60, 637 共1992兲.
9 P. Heller, R. Keith, and S. Anderson, Teaching problem solving
through cooperative grouping. Part 1: Groups versus individual
problem solving, Am. J. Phys. 60, 627 共1992兲.
10
W. J. Leonard, R. J. Dufrense, and J. P. Mestre, Using qualitative
problem solving strategies to highlight the role of conceptual
knowledge in solving problems, Am. J. Phys. 64, 1495 共1996兲.
11 F. Reif, Millikan Lecture 1994: Understanding and teaching important scientific thought processes, Am. J. Phys. 63, 17 共1995兲.
12 C. Bereiter and M. Scardamalie, in Handbook of Research on
Curriculum, edited by P. W. Jackson 共MacMillan, New York,
1992兲, p. 517.
13
J. S. Brown, A. Collins, and S. Duguid, Situated Cognition and
the Culture of Learning, Educ. Res. 18, 32 共1989兲.
14
A. Collins, J. S. Brown, and A. Holum, Cognitive apprenticeship:
Making thinking visible, Am. J. Educ., 6, 38 共1991兲.
15 A. Collins, J. S. Brown, and S. E. Newman, Knowing, Learning,
and Instruction: Essays in Honor of Robert Glaser, edited by L.
B. Resnick 共Erlbaum, Hillsdale, NJ, 1989兲.
16 S. Farnham-Diggory, Paradigms of Knowledge and Instruction,
Rev. Educ. Res. 64, 463 共1994兲.
17 K.
Cummings, J. Marx, R. Thornton, and D. Kuhl, Evaluating
innovation in studio physics, Am. J. Phys. 67, S38 共1999兲.
18
M. Prosser, K. Trigwell, and P. Taylor, A phenomenographic
study of academics’ conceptions of science learning and teaching, Learn. Instr. 4, 217 共1994兲.
19
J. B. Biggs, Approaches to enhancement of tertiary teaching,
Higher Educ. Res. Dev. 8, 7 共1989兲.
20
E. Martin and M. Balla, Conceptions of teaching and implications
for learning, Res. Higher Educ. 13, 298 共1991兲.
21
K. Trigwell, M. Prosser, F. Marton et al., in Teacher Thinking,
Beliefs and Knowledge in Higher Education, edited by N.
Hativa and P. Goodyear 共Kluwer, Dordrecht, The Netherlands,
2002兲, p. 241.
22
J. G. Donald, Professors’ and Students’ Conceptualizations of the
Learning Task in Introductory Physics Courses, J. Res. Sci.
Teach. 30, 905 共1993兲.
23 J. H. Van Driel, N. Verloop, H. I. Van Werven et al., Teachers’
craft knowledge and curriculum innovation in higher engineering education, J. Higher Educ. 34, 105 共1997兲.
24 J. Calderhead, in Handbook of Educational Psychology, edited by
D. C. Berliner and R. C. Calfee 共Prentice-Hall, New York,
1996兲, p. 709.
25 A. Lumpe, C. Czerniak, and J. Haney, Science teacher beliefs and
intentions regarding the use of cooperative learning, Sch. Sci.
Math. 98, 123 共1998兲.
26 E. Yerushalmi and B. Eylon, in Proceedings of the International
GIREP Conference on Physics Teacher Education beyond 2000
共GIREP, Barcelona, Spain, 2001兲.
27 I. Huibregtse, F. Korthagen, and T. Wubbels, Physics teachers’
conceptions of learning, teaching and professional development,
Int. J. Sci. Educ. 16, 539 共1994兲.
28
A. H. Schoenfeld, Towards a theory of teaching-in-context, Issues
Educ. Res. 4, 1 共1998兲.
29
D. C. Berliner, in Exploring Teachers’ Thinking, edited by J.
Calderhead 共Cassell Educational Limited, London, Great Britain, 1987兲, p. 60.
30 D. C. Berliner, in New Directions for Teacher Assessment (Proceedings of the 1988 ETS Invitational Conference), edited by J.
Pfleiderer 共Educational Testing Service, Princeton, NJ, 1988兲, p.
39.
31 K. Carter and W. Doyle, Teachers’ knowledge structures and
comprehension processes, J. Higher Educ. 59, 186 共1987兲.
32 M. J. Dunkin and R. P. Precians, Award-winning university teachers’ concepts of teaching, J. Higher Educ. 24, 483 共1992兲.
33
O. Kwo, in Teachers’ Minds and Actions: Research on Teachers’
Thinking and Practice, edited by I. Carlgren, G. Handal, and S.
Vaage 共Falmer Press, London, 1994兲, p. 215.
34 J. Mitchell and P. Marland, Research on teacher thinking: The
020109-29
PHYS. REV. ST PHYS. EDUC. RES. 3, 020109 共2007兲
YERUSHALMI et al.
next phase, Teach. Teach. Educ. 5, 115 共1989兲.
J. Piaget, The Child’s Conception of the World 共Harcourt, Brace,
New York, 1929兲.
36 J. Piaget, The Child’s Conception of Movement and Speed 共Routledge, London, 1970兲.
37 R. Driver, E. Guense, and A. Tiberghien, Children’s Ideas in Science 共Open University Press, Buckingham, UK, 1985兲.
38
R. Driver and J. Easley, Pupils and paradigms: a review of the
literature related to concept development in adolescent science
students, Stud. Sci. Educ. 5, 61 共1978兲.
39 J. H. Wandersee, J. J. Mintzes, and J. D. Novak, in Handbook of
Research on Science Teaching and Learning, edited by D. Gabel
共MacMillan, New York, 1994兲, p. 177.
40
L. McDermott, Research on conceptual understanding in mechanics, Phys. Today 37, 24 共1987兲.
41 S. Strauss, in Understanding and Teaching the Intuitive Mind,
edited by B. Torff and R. J. Sternberg 共Erlbaum, Mahwah, NJ,
2001兲, p. 217.
42 National Research Council, How People Learn: Brain, Mind, Experience, and School 共National Academy Press, Washington,
DC, 1999兲.
43
O. Lantz and H. Katz, Chemistry teachers’ functional paradigms,
Sci. Educ. 71 117 共1987兲.
44 J. Nespor, The role of beliefs in the practice of teaching, J. Curric.
Stud. 19, 317 共1987兲.
45 S. M. Wilson, L. S. Shulman, and A. E. Richert, in Exploring
Teachers’ Thinking, edited by J. Calderhead 共Cassell Educational
Limited, London, 1987兲.
46
M. F. Pajares, Teachers’ beliefs and education research: Cleaning
up a messy Construct, Rev. Educ. Res. 63, 307 共1992兲.
47
J. Hutchinson and M. Huberman, Knowledge dissemination and
use in science and mathematics education: literature review
共National Science Foundation, Arlington, VA, 1993兲.
48
R. Yerrick, H. Parke, and J. Nugent, Struggling to promote deeply
rooted change: The “Filtering effect” Of teachers’ beliefs on
understanding transformational views of teaching science, Int. J.
Sci. Educ. 81, 137 共1997兲.
49
J. W. Stigler and J. Hiebert, The Teaching Gap: Best Ideas from
the World’s Teachers for Improving Education in the Classroom
共The Free Press, New York, 1999兲.
50 D. Winter, P. Lemons, J. Bookman, and W. Hoese, Novice instructors and student-centered instruction: Identifying and addressing obstacles to learning in the college science laboratory,
J. Scholarship Teach. Learn. 2, 15 共2001兲.
51
M. I. Honig and T. C. Hatch, Crafting coherence: How schools
strategically manage multiple, external demands, Educ. Res. 33,
16 共2004兲.
52 J. P. Spillane, Standards Deviation: How Schools Misunderstand
Educational Policy 共Harvard University Press, Cambridge, MA,
2004兲.
53
F. Reif, Phys. Today 39, 48 共1986兲.
54
J. W. Creswell, Qualitative Inquiry and Research Design: Choosing among Five Traditions 共Sage, Thousand Oaks, CA, 1998兲.
55
R. J. Shavelson and P. Stern, Research on teachers’ pedagogical
thoughts, judgments, decisions, and behavior, Rev. Educ. Res.
51, 455 共1981兲.
56 A. L. Strauss, Qualitative Analysis for Social Scientists 共Cambridge University Press, Cambridge, 1987兲.
57 A. L. Strauss and J. Corbin, Basics of Qualitative Research:
Grounded Theory Procedures and Techniques 共Sage, Newbury
35
Park, CA, 1990兲.
C. Henderson, E. Yerushalmi, K. Heller, P. Heller, and V. Kuo,
Phys. Rev. ST Phys. Educ. Res. 3, 020110 共2007兲.
59 A. Schoenfeld, Mathematical Problem Solving 共Academic Press,
New York, 1985兲.
60
D. Maloney, in Handbook of Research on Science Teaching and
Learning, edited by D. Gabel 共MacMillan, New York, 1994兲.
61 P. Heller, T. Foster, and K. Heller, in The Changing Role of Physics Departments in Modern Universities: Proceedings of the International Conference on Undergraduate Physics Education,
edited by E. F. Redish and J. S. Rigden 共American Institute of
Physics, Woodbury, NY, 1996兲, p. 913.
62
F. Lawrenz, P. Heller, R. Keith, and K. Heller, Training the teaching assistant: Matching the ta strengths and capabilities to meet
specific program goals, J. Coll. Sci. Teach. 22, 106 共1992兲.
63 T. Foster, in Curriculum and Instruction 共University of Minnesota, Minneapolis, MN, 2000兲.
64
R. H. Hycner, Some guidelines for the phenomenological analysis
of interview data, Hum. Stud. 8, 279 共1985兲.
65 J. D. Novak and D. B. Gowin, Learning How to Learn 共Cambridge University Press, New York, 1984兲.
66
C. Henderson, E. Yerushalmi, V. Kuo, P. Heller, and K. Heller,
Grading Student Problem Solutions: The Challenge of Sending a
Consistent Message, Am. J. Phys. 72, 164 共2004兲.
67 M. Dancy and C. Henderson, in Proceedings of the 2004 AAPT
Physics Education Research Conference, edited by S. Franklin,
J. Marx, and P. Heron 共American Institute of Physics, Melville,
NY, 2005兲.
68 J. A. Michael and H. I. Modell, Active Learning in Secondary and
College Science Classrooms 共Lawrence Erlbaum, Mahwah, NJ,
2003兲.
69
J. D. Bransford et al., in Cognition, Education and Multimedia,
edited by D. Nix and R. Sprio 共Erlbaum Associates, Hillsdale,
NJ, 1990兲.
70 J. D. Bransford and B. S. Stein, The Ideal Problem Solver, 2nd
ed. 共Freeman, New York, 1993兲.
71 M. Cole, in Vygotsky and Education: Instructional Implications
and Applications of Sociohistorical Psychology, edited by L.
Moll 共Cambridge University Press, Cambridge, UK, 1990兲, pp
89–110.
72
P. Cobb and E. Yackel, Constructivist, emergent, and sociocultural perspectives in the context of development research, Educ.
Psychol. 31, 175 共1996兲.
73 G. Polya, How to Solve It 共Princeton University Press, Princeton,
1957兲.
74 H. L. Dreyfus and S. E. Dreyfus, Five Steps from Novice to Expert 共Free Press, New York, 1986兲.
75 H. L. Dreyfus and S. E. Dreyfus, in Advances in Cognitive Science, edited by N. E. Sharkey 共Ellis Horwood Limited, West
Sussex, England, 1986兲.
76 E. F. Redish, J. M. Saul, and R. N. Steinberg, Student expectations in introductory physics, Am. J. Phys. 66, 212 共1998兲.
77 P. R. Pintrich and E. V. D. Groot, Motivational and self-regulated
learning components of classroom academic performance, J.
Educ. Psychol. 82, 33 共1990兲.
78
E. Yerushalmi and E. Magen, Same old problem, new name?
Alerting students to the nature of the problem-solving process,
Phys. Educ. 41, 161 共2006兲.
58
020109-30
PHYSICS FACULTY BELIEFS AND… . I. …
79 R.
PHYS. REV. ST PHYS. EDUC. RES. 3, 020109 共2007兲
T. Putnam and H. Borko, What do new views of knowledge
and thinking have to say about research on teacher learning?,
Educ. Res. 29, 4 共2000兲.
80
S. Loucks-Horsley, P. Hewson, N. Love et al., Designing Professional Development for Teachers of Science and Mathematics
共Corwin Press, Thousand Oaks, CA, 1998兲.
81 National Research Council, The National Science Education
Standards 共The National Academies Press, Washington, DC,
1996兲.
L. Shulman, Those who understand: Knowledge growth in teaching, Educ. Res. 15, 4 共1986兲.
83
R. Sternberg and J. Horvath, A prototype view of expert teaching,
Educ. Res. 24, 9 共1995兲.
84
W. Lauden, in Understanding Teacher Development, edited by A.
Hargreaves and M. G. Fullan 共Teacher College Press, New York,
1992兲.
82
020109-31